NCERT Solutions Class 5 Maths Chapter 13 Animal Jumps

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 13: Animal Jumps

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

164 – 170 13 72 English

Solutions, notes, sample papers & more at 58 pages

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 13: Animal Jumps
Chapter 13 of Math Mela turns skip counting into a game of jumps. A rabbit jumps 4 at a time, a frog jumps 3,
a spider jumps 3, a grasshopper jumps 6 — and Mowgli hops along a forest trail to meet his friends. From
these jumps the chapter builds four big ideas: factors, multiples, common factors and common multiples.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 164 – 170

SECTIONS QUESTIONS

13 72

MEDIUM

English

Find the Hidden Numbers — Page 164
The multiplying box; factors, multiples and arrays

FIND THE HIDDEN NUMBERS

Q1 (a) Can you guess the multiplier if you see the 4 numbers coming out of the box?

The multiplier can be 1, 2 or 4.
The box does the same thing to every number put in — it multiplies it. So the multiplier must fit
exactly into all four numbers that came out: 28, 36, 48 and 72.

1. List every number that divides 28 exactly. 1, 2, 4, 7, 14, 28.
2. Do the same for 36. 1, 2, 3, 4, 6, 9, 12, 18, 36.
3. Do the same for 48. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
4. Do the same for 72. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
5. Tick the numbers that are in all four lists. Only 1, 2 and 4 are in every list.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

28 = 4 × 7

36 = 4 × 9

48 = 4 × 12
72 = 4 × 18

So the multiplier can be 4 (and also 2, or 1)

Why it happens: A number that divides another number exactly, with nothing left
over, is called a factor. The multiplier had to be a factor of every number that came
out, because the box built each of those numbers by multiplying. So the answer is
the list of factors that 28, 36, 48 and 72 all share.

Tip: 4 is the most interesting guess, because it is the biggest of the three. A
multiplier of 1 would mean the box did nothing at all.

Q2 (b) Is there more than one possible multiplier?

Yes. There are three possible multipliers: 1, 2 and 4.

MULTIPLIER DOES IT DIVIDE 28, 36, 48 AND 72 EXACTLY?

1 Yes — 1 divides every number

2 Yes — all four numbers are even

4 Yes — 28 = 4 × 7, 36 = 4 × 9, 48 = 4 × 12, 72 = 4 × 18

3 No — 28 ÷ 3 leaves 1 over

6 No — 28 ÷ 6 leaves 4 over

Why it happens: 1, 2 and 4 are the common factors of 28, 36, 48 and 72 — the
factors that all four numbers share. Any one of them could have been the multiplier.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Check it yourself: Try 8. 48 ÷ 8 = 6 and 72 ÷ 8 = 9, but 28 ÷ 8 leaves 4 over. So 8 fails,
and it is not a common factor.

Q3 (c) What numbers might have been put inside the box?

It depends on which multiplier the box was using. Here are all three sets.

IF THE MULTIPLIER THEN THE NUMBERS PUT IN WORKING
IS… WERE…

4 7, 9, 12, 18 28 ÷ 4 = 7, 36 ÷ 4 = 9, 48 ÷ 4 = 12, 72 ÷
4 = 18

2 14, 18, 24, 36 28 ÷ 2 = 14, 36 ÷ 2 = 18, 48 ÷ 2 = 24,
72 ÷ 2 = 36

1 28, 36, 48, 72 Nothing changes when you multiply
by 1

To go backwards, divide.

Number that came out ÷ multiplier = number that went in

28 ÷ 4 = 7

Why it happens: Multiplying and dividing undo each other. The box multiplied, so to
find what went in you divide.

Look at the picture again: Faint numbers are drawn near the box in your book —
12, 7 and 18 are three of them. All three are in the answer for a multiplier of 4.

Q4 Share your thoughts in the class. You can also play this game with your friends.

Sample answer: The box must be multiplying by 4. All four numbers that came out — 28, 36, 48
and 72 — can be split into equal groups of 4 with nothing left over. So the numbers that went in
were 7, 9, 12 and 18. A multiplier of 2 also works, and even 1 works, but 1 would mean the box

Page 3 of 58

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

changed nothing.
co m
How to play it with your friends, step by step:
se m.
o m l a
m .c is the box. That player secretly chooses a multiplier, saya6.g
1. One player
e call out numbers. Say they call out 3, 5 and 8.
2. Thesothers
a
l
agThe box answers. The box says 18, 30 and 48 — each number multiplied by 6.
3.

m
4. Guess the multiplier. Look for the biggest number that divides 18, 30 and 48 exactly. It is 6.

. co ag
m
5. Swap roles and play again.

l a se
ag by choosing a multiplier like 7 or 9. The numbers
Try This: Make the game harder
that come out grow fast, and your friends must hunt for factors instead of guessing.

co m
em.
m l as
.co a g
a
Q5
s em A number, when arranged in an array, shows the factors of that number. Are there

ag l other numbers that are factors of 15? Try to make other arrays for the number 15.

om a s
c agl
.
m 15 are also factors of 15. So 15 has four factors in
s e
Yes. Besides 3 and 5, the numbers 1 and
all: 1, 3, 5 and 15.
a gla
An array means the counters set out in equal rows, in a rectangle. Each rectangle you can make
gives you a pair of factors.
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m 3 × 5 = 15 as e
.co a g l
se m
g l a
a c
m .
s e
. com 5 × 3 = 15 agl
a
se m
l a
ag for 15. Both use 15 counters — one is the other turned round.
Two rectangles

co m
m .
m ase
.co


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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

1 × 15 = 15
A third rectangle: one single row of 15. This one gives the factors 1 and 15.

3 × 5 = 15 → factors 3 and 5

5 × 3 = 15 → the same two factors

1 × 15 = 15 → factors 1 and 15

Factors of 15 = 1, 3, 5, 15

Why it happens: If the counters fit into a neat rectangle with no gaps, then the
number of rows divides the total exactly. That is exactly what a factor is. A rectangle
you cannot make — say 4 rows of something — means 4 is not a factor of 15.

Check it yourself: Try 2 rows. 15 counters cannot be split into 2 equal rows — one
row would be 7 and the other 8. So 2 is not a factor of 15.

Q6 Let us make arrays for the number 12. (The book shows 3 × 4 = 12, 2 × 6 = 12 and 1 ×
12 = 12.) Which numbers are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12 — six factors in all.

Page 5 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

2 × 6 = 12
3 × 4 = 12
Two of the rectangles the book draws for 12.

1 × 12 = 12
The third rectangle: one long row of 12.

Every rectangle hands you a pair of factors. Collect the pairs:

1 × 12 = 12 → 1 and 12

2 × 6 = 12 → 2 and 6

3 × 4 = 12 → 3 and 4

Factors of 12 = 1, 2, 3, 4, 6, 12

Why it happens: Turning a rectangle on its side gives the same pair of factors. 3
rows of 4 and 4 rows of 3 both use 12 counters, so they tell us the same thing. That
is why we only need three rectangles to find all six factors.

Page 6 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Tip: To hunt for factors, try 1, then 2, then 3, then 4 … and stop when the numbers
start repeating. For 12, after 3 × 4 the next try is 4 × 3, which we already have — so
you can stop.

Why 12 is a Multiple — Page 165
1, 2, 3, 4, 6 and 12 are all factors of 12

Q1 1, 2, 3, 4, 6, and 12 are all factors of 12. Each of the numbers can divide 12
completely. 12 is a multiple of these numbers. Do you see why 12 is a multiple of 1,
2, 3, 4, 6, and 12?

Yes. 12 is a multiple of each of them because each one divides 12 exactly, with nothing left
over.
Think of it as jumping. Start at 0 and take equal jumps. If you land exactly on 12, then your jump
size is a factor of 12, and 12 is a multiple of your jump size.

JUMP SIZE JUMPS NEEDED TO REACH 12 MULTIPLICATION DIVISION

1 12 jumps 1 × 12 = 12 12 ÷ 1 = 12

2 6 jumps 2 × 6 = 12 12 ÷ 2 = 6

3 4 jumps 3 × 4 = 12 12 ÷ 3 = 4

4 3 jumps 4 × 3 = 12 12 ÷ 4 = 3

6 2 jumps 6 × 2 = 12 12 ÷ 6 = 2

12 1 jump 12 × 1 = 12 12 ÷ 12 = 1

Jumps of 3 land on 12
Jumps of 4 also land on 12

0 1 2 3 4 5 6 7 8 9 10 11 12

Both jump sizes land exactly on 12. So 3 and 4 are factors of 12, and 12 is a multiple of both.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: The words factor and multiple are two ways of describing the same
fact. In 3 × 4 = 12, the numbers 3 and 4 are the factors and 12 is the multiple. Factor
is the jump; multiple is the landing spot.

Tip for remembering: Factors are never bigger than the number. Multiples are
never smaller than the number.

Q2 Fill in the blanks: 2 × ____ = 12, 3 × ____ = 12, 12 × ____ = 12, 1 × ____ = 12

Here are the four answers.

2 × 6 = 12

3 × 4 = 12

12 × 1 = 12

1 × 12 = 12

How to find each missing number:

1. Divide 12 by the number you are given. For the first one, 12 ÷ 2 = 6.
2. Write the answer in the blank. 2 × 6 = 12.
3. Check by multiplying back. 2 × 6 = 12 ✓
4. Do the same for the rest. 12 ÷ 3 = 4, 12 ÷ 12 = 1, 12 ÷ 1 = 12.

The red note in your book says: The number itself is always a multiple of itself. That is
what 12 × 1 = 12 shows. Jump 12 steps once, and you land on 12. In the same way, 7
is a multiple of 7, and 100 is a multiple of 100.

Let Us Do — Page 165

Page 8 of 58

ase
Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

Make different arrays for the following numbers. Identify the factors in each case.
co m
em.
m as
LET US DO

.co a g l
a s em
gl
(a) 10
a
Q1

m
.co ag

Factors of 10: 1, 2, 5, 10. That is 4 factors inm
se
all.
l a
ag

co m
sem.
m a
m .co agl
1 × 10 = 10
l a se 2 × 5 = 10
a g
m
Arrays for 10. Each rectangle gives a pair of factors.
a s
m.co agl
l a se
ag
1 × 10 = 10 → factors 1 and 10

m
2 × 5 = 10 → factors 2 and 5
. co
em
All.c omfactors of 10 = 1, 2, 5, 10 g l as
m
the
a
ase
agl
Why it happens: 10 counters can be set out as one row of 10, or as 2 rows of 5. They
se m
com g l a
.
cannot be set out as 3 equal rows or 4 equal rows, so 3 and 4 are not factors of 10.
m a
ase
agl
Check it yourself: 2 × 5 = 10 and 1 × 10 = 10. Multiply each pair — both give 10 ✓

co m
m .
m(b) 14 as e
.co
Q2
a g l
a s em
agl ANSWER
.c
s e m
m a
Factors of 14: 1, 2, 7, 14. That is 4 factors in all.

em . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 9 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

1 × 14 = 14
2 × 7 = 14

Arrays for 14. Each rectangle gives a pair of factors.

1 × 14 = 14 → factors 1 and 14

2 × 7 = 14 → factors 2 and 7

All the factors of 14 = 1, 2, 7, 14

Why it happens: 14 is even, so it splits into 2 equal rows of 7. After that nothing else
works — 3, 4, 5 and 6 all leave counters over.

Q3 (c) 13

Factors of 13: 1, 13. That is 2 factors in all.

1 × 13 = 13
Only one rectangle is possible for 13 — a single row.

1 × 13 = 13 → factors 1 and 13

All the factors of 13 = 1, 13

Page 10 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 13 counters can only be laid out as one single row. Try 2 rows —
you get 6 and 7, which are not equal. Try 3 rows, 4 rows, 5 rows, 6 rows — every time
some counters are left over. So 13 has only two factors.

Did you know? A number with exactly two factors, 1 and itself, is called a prime
number. 13 is prime.

Q4 (d) 20

Factors of 20: 1, 2, 4, 5, 10, 20. That is 6 factors in all.

2 × 10 = 20

4 × 5 = 20
Arrays for 20. Each rectangle gives a pair of factors.

1 × 20 = 20 → factors 1 and 20

2 × 10 = 20 → factors 2 and 10

4 × 5 = 20 → factors 4 and 5

All the factors of 20 = 1, 2, 4, 5, 10, 20

Why it happens: Test the numbers one by one. 20 ÷ 1 = 20 ✓, 20 ÷ 2 = 10 ✓, 20 ÷ 3
leaves 2 over ✗, 20 ÷ 4 = 5 ✓, 20 ÷ 5 = 4 ✓. After 4 × 5 the pairs start repeating, so
you can stop.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q5 (e) 25

Factors of 25: 1, 5, 25. That is 3 factors in all.

5 × 5 = 25
25 counters make a perfect square: 5 rows of 5.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

1 × 25 = 25 → factors 1 and 25

5 × 5 = 25 → factors 5 and 5

All the factors of 25 = 1, 5, 25

The other rectangle is one row of 25 counters, which gives the factors 1 and 25.

Why it happens: 25 makes a perfect square — 5 rows of 5. When a number makes a
square array, the two factors in that pair are the same number, so it gets counted
only once. That is why 25 has an odd number of factors: three.

Try This: Which other numbers make a perfect square array? 4 (2 × 2), 9 (3 × 3), 16 (4
× 4), 36 (6 × 6).

Q6 (f) 32

Factors of 32: 1, 2, 4, 8, 16, 32. That is 6 factors in all.

2 × 16 = 32

4 × 8 = 32

Arrays for 32. Each rectangle gives a pair of factors.

1 × 32 = 32 → factors 1 and 32

2 × 16 = 32 → factors 2 and 16

4 × 8 = 32 → factors 4 and 8

All the factors of 32 = 1, 2, 4, 8, 16, 32

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: 32 keeps halving: 32, 16, 8, 4, 2, 1. Every one of those is a factor. No

m as e
l
odd number except 1 divides 32, because 32 is made only of 2s: 2 × 2 × 2 × 2 × 2 = 32.

m .co a g
l a se
a g
Q7 (g) 37

com
m . ag
l a se
agin all.
Factors of 37: 1, 37. That is 2 factors

co m
em.
m l as
m .co 1 × 37 = 37 a g
ase
agl 37 counters make only one rectangle — a single long row.

m a s
m .co agl
a se
1 × 37 = 37 → factors 1 and 37

a g l

m
All the factors of 37 = 1, 37
. co
se m
o m l a
m .c it happens: Try 2 rows, 3 rows, 4 rows, 5 rows, 6 rowsag— every single time some
Why
asecounters are left over. Only one long row works.
agl
se m
Did you know? 37 is a prime number, just like 13.
com g l a
m . a
ase
agl
(h) 46
m
Q8

. co
em
com of 46: 1, 2, 23, 46. That is 4 factors in all.
g l as
. a
sem
Factors
a
agl c
m .
m a s e
e m . co agl
g l as
a 2 × 23 = 46

com
m .
m ase
.co


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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

46 counters as 2 rows of 23. The other rectangle is one row of 46.

1 × 46 = 46 → factors 1 and 46

2 × 23 = 46 → factors 2 and 23

All the factors of 46 = 1, 2, 23, 46

Why it happens: 46 is even, so 2 rows of 23 work. After that, 3, 4, 5 … up to 22 all
leave counters over, because 23 is itself a prime number.

Q9 (i) 54

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. That is 8 factors in all.

3 × 18 = 54

6 × 9 = 54

Arrays for 54. Each rectangle gives a pair of factors.

1 × 54 = 54 → factors 1 and 54

2 × 27 = 54 → factors 2 and 27

3 × 18 = 54 → factors 3 and 18
6 × 9 = 54 → factors 6 and 9

All the factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

Page 15 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 54 is even, so 2 is a factor. 5 + 4 = 9, and 9 is in the 3 times table, so
3 is a factor too. Working through the pairs gives 1 × 54, 2 × 27, 3 × 18 and 6 × 9 —
eight factors in all.

Check it yourself: 6 × 9 = 54 ✓ and 3 × 18 = 54 ✓

Q10 Numbers like 13 and 37 are called prime numbers. Why?

Because 13 and 37 have exactly two factors each — 1 and the number itself. Nothing else
divides them.
You can see it in the arrays. Most numbers make more than one rectangle. 13 and 37 make only
one: a single long row.

NUMBER RECTANGLES YOU CAN MAKE FACTORS PRIME?

10 1 × 10, 2 × 5 1, 2, 5, 10 No — four factors

13 1 × 13 only 1, 13 Yes

14 1 × 14, 2 × 7 1, 2, 7, 14 No

37 1 × 37 only 1, 37 Yes

Why it happens: To check whether 13 is prime, try to share 13 counters into equal
groups. Groups of 2 leave 1 over. Groups of 3 leave 1 over. Groups of 4, 5 and 6 all
leave some over. Since nothing between 2 and 12 divides 13, the only factors left are
1 and 13.

Tip: The prime numbers below 40 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37.
Notice that 1 is not prime — it has only one factor, not two.

Animal Jumps — Page 165

Page 16 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

A rabbit jumps 4, a frog jumps 3 — where do they meet?

ANIMAL JUMPS DISCUSS IN CLASS

Q1 A rabbit takes a jump of 4 each time. A frog takes a jump of 3 each time. Use the
number line to figure out the numbers they will both touch. If the rabbit and the
frog start from 0, the numbers both of them will touch are called the common
multiples of 3 and 4.

Frog: jumps of 3 Rabbit: jumps of 4

0 3 4 6 8 9 12

Page 165 — the number line. Both animals start at 0. The frog’s first jump is shown in
blue and the rabbit’s first jump in red.

Between 0 and 12 they both touch only one number — 12.

Frog: jumps of 3
Rabbit: jumps of 4

0 1 2 3 4 5 6 7 8 9 10 11 12

The frog lands on 3, 6, 9, 12. The rabbit lands on 4, 8, 12. The circled 12 is the only spot they share.

1. Draw the frog's jumps. Starting at 0 and jumping 3: 3, 6, 9, 12.
2. Draw the rabbit's jumps. Starting at 0 and jumping 4: 4, 8, 12.
3. Look for a number in both lists. Only 12 is in both.

Page 17 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Frog (3s): 3, 6, 9, 12

Rabbit (4s): 4, 8, 12

First common landing spot = 12

Why it happens: 12 is in the 3 times table (3 × 4 = 12) and also in the 4 times table (4
× 3 = 12). A number that is a multiple of both numbers is called a common multiple.
The word "common" here just means "shared".

Tip: The frog reaches 12 in 4 jumps; the rabbit reaches it in 3 jumps. They both get
there, but the rabbit gets there first because its jumps are longer.

Q2 12 is the first common multiple of 3 and 4. What are some other common multiples
of 3 and 4? You can continue the number line or take help from the times tables of 3
and 4.

Frog: jumps of 3 Rabbit: jumps of 4

0 3 4 6 8 9 12

Page 165 — the number line. Both animals start at 0. The frog’s first jump is shown in
blue and the rabbit’s first jump in red.

The next common multiples are 24, 36, 48, 60 and 72 — and they go on for ever.

MULTIPLES OF 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48 …

MULTIPLES OF 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 …

COMMON MULTIPLES 12, 24, 36, 48, 60, 72 …

Page 18 of 58

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

1. Write the 3 times table. 3, 6, 9, 12, 15, 18, 21, 24 …
co m
2. Write the 4 times table below it. 4, 8, 12, 16, 20, 24 …
e m.
m l as
.co a g
3. Circle every number that appears in both rows. 12, 24, 36, 48 …

a s em
gl× 1 = 12
a12
m
12 × 2 = 24
. co ag
e m
as
12 × 3 = 36

12 × 4 = 48 a g l

m
12 × 5 = 60
co
se m.
o m l a
Why it.chappens: Once the frog and the rabbit meet at 12, thegwhole pattern starts
e m a
l a s
again from there. So they meet again 12 steps later at 24, then at 36, and so on —
a g every 12 steps.

m a s
m .co agl
l a se
Q3
a g
What do you notice about the common multiples of 3 and 4? Discuss in class.

. c om
Sample answer: Every common multiple of 3 and 4 is a multiple of 12. The
s e mlist is simply the 12
c om— 12, 24, 36, 48, 60 … The smallest one is 12, and every a one is made by adding
glother
.
times table
12em
a
a s again and again. There is no biggest one; the list never ends.

agl Three things the class should notice:
se m
comthe two numbers multiplied together. a
1. The first common multiple is 12, and 12 = 3 × 4. When two numbers share no factor except

.
1, their first common multiple is simply
a g l
s m first one. 24 = 12 × 2, 36 = 12 × 3, 48 = 12 × 4.
ethe
a
l numbers always have endless common multiples — unlike
2. All the others are multiples of

agTwo
3. The list goes on for ever.
common factors, of which there are only a few.

. c om
Why it happens: To land on the same spot, the number mustem
m a s be reachable by 3-

.cjumps agltable can do both, because
o and by 4-jumps. Only the numbers in the 12 times
m 12 is the smallest number that both 3 and 4 divide exactly.
l a se
ag
.c
s e m
om a
.c 166
Spider and Grasshopper —mPage
e agl
g l as
a

com
m .
m ase
.co


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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

A spider jumps 3, a grasshopper jumps 6; then the multiples of 4 and 6

DISCUSS IN CLASS

Q1 A spider takes a jump of 3 every time. A grasshopper takes a jump of 6 each time.
Use the number line to find the common multiples of 3 and 6.

Spider: jumps of 3 Grasshopper: jumps of 6

0 3 6 9 12

Page 166 — the number line. Both start at 0. The spider’s first jump is shown in green
and the grasshopper’s first jump in purple.

They land together on 6, 12, 18, 24 … — that is, on every multiple of 6.

Spider: jumps of 3
Grasshopper: jumps of 6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

The spider touches 3, 6, 9, 12, 15, 18. The grasshopper touches 6, 12, 18. Every grasshopper spot is
also a spider spot.

Spider (3s): 3, 6, 9, 12, 15, 18

Grasshopper (6s): 6, 12, 18

Common multiples of 3 and 6 = 6, 12, 18, 24, 30 …

Page 20 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: The grasshopper's jump of 6 is exactly two of the spider's jumps of
3. So wherever the grasshopper lands, the spider has just landed too. That is why
every single grasshopper spot is shared.

Tip: Here the first common multiple is 6 — the bigger of the two numbers. This
always happens when one number is a multiple of the other.

Q2 6 and 12 are two common multiples of 3 and 6. You can continue the pattern to find
more common multiples. What do you notice about the common multiples of 3 and
6? Discuss.

Spider: jumps of 3 Grasshopper: jumps of 6

0 3 6 9 12

Page 166 — the number line. Both start at 0. The spider’s first jump is shown in green
and the grasshopper’s first jump in purple.

Sample answer: The common multiples of 3 and 6 are 6, 12, 18, 24, 30, 36 … They are exactly
the multiples of 6 — the grasshopper's own list. Nothing new has to be worked out, because 6 is
already a multiple of 3.
What the class should notice:

1. The first common multiple is 6, which is the bigger of the two numbers.
2. The grasshopper's list is completely inside the spider's list. Every multiple of 6 is also a
multiple of 3.
3. The pattern continues for ever — 36, 42, 48, 54, 60 …

Why it happens: 6 = 3 × 2. So a jump of 6 is just two jumps of 3 joined together. The
grasshopper can never land anywhere the spider has not already been.

Page 21 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Compare with the last page: For 3 and 4 the first common multiple was 12 = 3 × 4.
For 3 and 6 it is only 6, not 18. The difference is that 6 is a multiple of 3, while 4 is
not.

Q3 Let us write the multiples of two numbers — 4 and 6. Multiples of 4: 4, 8, 12, 16, …
Multiples of 6: 6, 12, 18, … 12 and 24 are two of the common multiples of 4 and 6. List
a few more.

A few more common multiples of 4 and 6 are 36, 48, 60, 72 and 84.

MULTIPLES OF 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 …

MULTIPLES OF 6 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 …

COMMON MULTIPLES 12, 24, 36, 48, 60, 72, 84 …

1. Write both times tables side by side.
2. Circle the numbers that appear in both. 12, 24, 36, 48, 60 …
3. Look at the pattern. Each one is 12 more than the one before, so you can keep adding 12.

12 + 12 = 24

24 + 12 = 36

36 + 12 = 48

48 + 12 = 60

60 + 12 = 72

Why it happens: 4 and 6 both divide 12 exactly, and 12 is the smallest number they
both divide. So every common multiple is a step of 12 along the number line.

Let Us Do (Question 1) — Page 166

Page 22 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Find 5 common multiples of the following pairs of numbers.

LET US DO DISCUSS IN CLASS

Q1 (a) 2 and 3

Five common multiples of 2 and 3 are 6, 12, 18, 24, 30.

MULTIPLES OF 2 2, 4, 6, 8, 10, 12 …

MULTIPLES OF 3 3, 6, 9, 12 …

COMMON MULTIPLES 6, 12, 18, 24, 30 …

1. Write the 2 times table.
2. Write the 3 times table under it.
3. Circle the numbers that appear in both. The smallest is 6.
4. Keep adding 6. 6 → 12 → 18 → 24 → 30

Why it happens: 2 and 3 share no factor except 1. When that happens, the first
common multiple is simply the two numbers multiplied together: 2 × 3 = 6.

A note on the book: In this list your book prints the label (f) twice — once for "9 and
12" and again for "8 and 12". So there are nine pairs in all, even though the last label
reads (h). We have answered all nine, in the order they are printed.

Q2 (b) 5 and 8

Five common multiples of 5 and 8 are 40, 80, 120, 160, 200.

MULTIPLES OF 5 5, 10, 15, 20, 25, 30, 35, 40, 45 …

MULTIPLES OF 8 8, 16, 24, 32, 40, 48, 56, 64, 72 …

COMMON MULTIPLES 40, 80, 120, 160, 200 …

1. Write the 5 times table.
2. Write the 8 times table under it.

Page 23 of 58

as e
Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

3. Circle the numbers that appear in both. The smallest is 40.
co m
4. Keep adding 40. 40 → 80 → 120 → 160 → 200
e m.
m l as
.co a g
a s em
Why it happens: 5 and 8 share no factor except 1. When that happens, the first
gl
acommon multiple is simply the two numbers multiplied together: 5 × 8 = 40.

co m
e m . ag
Q3 (c) 2 and 4
g l as
a

co m

Five common multiples of 2 and 4 are 4, 8, 12, 16, 20.
em.
comOF 2 g l as
. a
s em
MULTIPLES 2, 4, 6, 8 …

a
aglMULTIPLES OF 4 4, 8 …

m a s
.co agl
COMMON MULTIPLES 4, 8, 12, 16, 20 …

se m
g l a
a
1. Write the 2 times table.
2. Write the 4 times table under it.
3. Circle the numbers that appear in both. The smallest is 4.
co m
m .
e
4. Keep adding 4. 4 → 8 → 12 → 16 → 20

m l as
.co a g
a s emWhy it happens: 4 is already a multiple of 2, so every multiple of 4 is also a multiple

agl of 2. That is why the first common multiple is 4 itself — the bigger number.
se m
com g l a
m . a
ase
agl
Q4 (d) 3 and 9

m

. co
m
Five common multiples of 3 and 9 are 9, 18, 27, 36, 45.

a se
com
.MULTIPLES l
9,g12, 15, 18 …
3, 6,a
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OF 3

a s
agl
c
MULTIPLES OF 9
.
9, 18 …

s e m
m a
.co agl
COMMON MULTIPLES 9, 18, 27, 36, 45 …

se m
1. Write the 3 times table.
g l a
a
2. Write the 9 times table under it.

m
3. Circle the numbers that appear in both. The smallest is 9.

. co
e m
m l as
.co a g
Page 24 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

4. Keep adding 9. 9 → 18 → 27 → 36 → 45

Why it happens: 9 is already a multiple of 3, so every multiple of 9 is also a multiple
of 3. That is why the first common multiple is 9 itself — the bigger number.

Q5 (e) 5 and 10

Five common multiples of 5 and 10 are 10, 20, 30, 40, 50.

MULTIPLES OF 5 5, 10, 15, 20 …

MULTIPLES OF 10 10, 20 …

COMMON MULTIPLES 10, 20, 30, 40, 50 …

1. Write the 5 times table.
2. Write the 10 times table under it.
3. Circle the numbers that appear in both. The smallest is 10.
4. Keep adding 10. 10 → 20 → 30 → 40 → 50

Why it happens: 10 is already a multiple of 5, so every multiple of 10 is also a
multiple of 5. That is why the first common multiple is 10 itself — the bigger number.

Q6 (f) 9 and 12

Five common multiples of 9 and 12 are 36, 72, 108, 144, 180.

MULTIPLES OF 9 9, 18, 27, 36, 45, 54, 63, 72 …

MULTIPLES OF 12 12, 24, 36, 48, 60, 72 …

COMMON MULTIPLES 36, 72, 108, 144, 180 …

1. Write the 9 times table.
2. Write the 12 times table under it.
3. Circle the numbers that appear in both. The smallest is 36.
4. Keep adding 36. 36 → 72 → 108 → 144 → 180

Page 25 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 9 and 12 share the factor 3. So their first common multiple is not 9
× 12 = 108, but the smaller number 36. After that you add 36 each time.

Q7 (f) 8 and 12

Five common multiples of 8 and 12 are 24, 48, 72, 96, 120.

MULTIPLES OF 8 8, 16, 24, 32, 40, 48 …

MULTIPLES OF 12 12, 24, 36, 48 …

COMMON MULTIPLES 24, 48, 72, 96, 120 …

1. Write the 8 times table.
2. Write the 12 times table under it.
3. Circle the numbers that appear in both. The smallest is 24.
4. Keep adding 24. 24 → 48 → 72 → 96 → 120

Why it happens: 8 and 12 share the factor 4. So their first common multiple is not 8
× 12 = 96, but the smaller number 24. After that you add 24 each time.

Q8 (g) 6 and 8

Five common multiples of 6 and 8 are 24, 48, 72, 96, 120.

MULTIPLES OF 6 6, 12, 18, 24, 30, 36, 42, 48 …

MULTIPLES OF 8 8, 16, 24, 32, 40, 48 …

COMMON MULTIPLES 24, 48, 72, 96, 120 …

1. Write the 6 times table.
2. Write the 8 times table under it.
3. Circle the numbers that appear in both. The smallest is 24.
4. Keep adding 24. 24 → 48 → 72 → 96 → 120

Page 26 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 6 and 8 share the factor 2. So their first common multiple is not 6 ×
8 = 48, but the smaller number 24. After that you add 24 each time.

Q9 (h) 6 and 9

Five common multiples of 6 and 9 are 18, 36, 54, 72, 90.

MULTIPLES OF 6 6, 12, 18, 24, 30, 36 …

MULTIPLES OF 9 9, 18, 27, 36 …

COMMON MULTIPLES 18, 36, 54, 72, 90 …

1. Write the 6 times table.
2. Write the 9 times table under it.
3. Circle the numbers that appear in both. The smallest is 18.
4. Keep adding 18. 18 → 36 → 54 → 72 → 90

Why it happens: 6 and 9 share the factor 3. So their first common multiple is not 6 ×
9 = 54, but the smaller number 18. After that you add 18 each time.

Q10 What do you notice about the common multiples of different pairs of numbers?
Discuss in class.

Sample answer: Every pair of numbers has endless common multiples. The smallest one
matters most — once you have it, all the others come from adding it again and again. And the
smallest one follows a pattern, depending on how the two numbers are related.

Page 27 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

KIND OF PAIR EXAMPLES FROM THIS FIRST COMMON MULTIPLE
EXERCISE

One number is a multiple of 2 and 4, 3 and 9, 5 and 10 The bigger number itself — 4, 9, 10
the other

The two share nothing except 1 2 and 3, 5 and 8 The two multiplied — 6, 40

The two share a factor bigger 8 and 12, 6 and 8, 6 and 9, 9 and 12 Smaller than the product — 24, 24,
than 1 18, 36

Three things to notice:

1. There is always a smallest common multiple, but never a biggest one. The list goes on
for ever.
2. Every common multiple is a multiple of the smallest one. For 6 and 8 the list is 24, 48, 72,
96 — the 24 times table.
3. Common multiples are never smaller than the bigger of the two numbers.

Why it happens: A common multiple is a spot both animals can land on. Once they
have met once, both patterns start again from that spot, so they will meet again
after the same gap — over and over, for ever.

Let Us Do (Questions 2–3) — Page 167
The cobbled road to the food, and Mowgli's forest trail

LET US DO

Q1 2. Food is available at the end of a cobbled road. Robby, the rabbit, takes a jump of 4
each time. Deeku, the deer, takes a jump of 6 each time. They both start at 0. Will
both Robby and Deeku reach the food? Who will reach first? How do you know?
Explain your answer.

No — only Robby reaches the food. Deeku never lands on it. The cobbled road in the book
runs from 0 to 64, and the food is at the last stone, 64.

Page 28 of 58

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

co m
em. Food at 64

omrabbit: jumps of 4
Robby.cthe g l as
0 em
a
a s 16 32 48

a gl

co m36
. ag
0 12 24 48 60 66

em
as
Deeku the deer: jumps of 6

a g l
Red dots are Robby's landing stones, blue dots are Deeku's. A red dot sits on 64. The blue dots jump
straight over it, from 60 to 66.

co m
e m.
m l as
.co
Step by step:
a g
s em
1. Check Robby. Divide 64 by his jump size. 64 ÷ 4 = 16, with nothing left over. So Robby lands
a
gl
a 2. Check Deeku. 64 ÷ 6 = 10 with 4 left over. So Deeku lands on 60, and his next jump takes him
exactly on 64, on his 16th jump.

om Deeku does not. So Robby reaches first, and in a s
agl
to 66 — right over the food.
3. Answer both parts. Robby reaches the.c
em
food.
fact he is the only one who gets a s
agl
there.

Robby: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64 ✓
co m
.
s em
Deeku: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66 ✗ (60, then straight to 66)
m a
. co a gl
em
as Why it happens: An animal can only land on a number that its jump size divides
a g l
exactly. 64 is a multiple of 4, so 4-jumps reach it. 64 is not a multiple of 6, so 6-jumps
se m
must skip over it.
com g l a
m . a
ase
agl
Check it yourself: 4 × 16 = 64 ✓. Now try 6 × 10 = 60 and 6 × 11 = 66. There is no
whole number that gives 64 when multiplied by 6.

co m
m .
o m l a se
.c 3. Mowgli's friends live along the trail on the marked
a gplaces below. Which of his
s e m
a
Q2

agl
friends will he be able to visit, if he jumps by 2 steps starting from 0?

.c
s e m
m a
co agl

m .
ase
He can visit the friends standing on even numbers: the ant at 4, the frog at 12, the bird at

a g l
14, the tiger at 26, Baloo the bear at 30 and the rabbit at 50.

co m
m .
m as e
.co


a g l Page 29 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Green = Mowgli lands here (jumps of 2) · Grey = he jumps over

Mowgli Spider Bird Tiger Akela Rabbit
0 9 14 26 35 50

4 12 21 30 39 57
Ant Frog Kaa Baloo Deer Monkey

Jumping 2 at a time from 0, Mowgli lands only on even numbers. The grey friends stand on odd
numbers, so he passes them by.

FRIEND STANDS ON EVEN OR ODD? DOES MOWGLI MEET HIM?

Ant 4 Even Yes

Spider 9 Odd No

Frog 12 Even Yes

Bird 14 Even Yes

Kaa the snake 21 Odd No

Sher Khan the tiger 26 Even Yes

Baloo the bear 30 Even Yes

Akela the wolf 35 Odd No

Deer 39 Odd No

Rabbit 50 Even Yes

Monkey 57 Odd No

Mowgli's landing spots: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 … 56, 58

These are the multiples of 2 — all the even numbers

Why it happens: Starting at 0 and adding 2 each time can only ever give an even
number. An odd number is one more than an even number, so a 2-jump can never
stop on it.

Page 30 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

What your book says: On the next page the book names four of these friends —
the ant, the frog, the bird and the rabbit, at 4, 12, 14 and 50 — and says that 2 is a
common factor of those numbers. The tiger at 26 and Baloo at 30 are on even
numbers too, so Mowgli passes them as well.

Mowgli's Jumps and Common Factors — Page 168
Jumps of 2, 3, 5 and 10 along the trail

A COMMON FACTOR OF TWO OR MORE NUMBERS EXACTLY DIVIDES EACH OF THE NUMBERS

Q1 Did Mowgli meet the ant, frog, bird and the rabbit? Notice their positions— 4, 12, 14,
and 50. 2 is a common factor of these numbers.

Yes, he met all four of them. Their houses stand on 4, 12, 14 and 50, and every one of those
numbers is even.

4 ÷ 2 = 2, nothing left over

12 ÷ 2 = 6, nothing left over

14 ÷ 2 = 7, nothing left over

50 ÷ 2 = 25, nothing left over

So 2 is a common factor of 4, 12, 14 and 50

Why it happens: A common factor of some numbers is a number that divides every
one of them exactly. Here the jump size is 2, and 2 goes into 4, 12, 14 and 50 with
nothing left over — which is exactly why Mowgli's 2-jumps land on all four houses.

Say it the other way round: 4, 12, 14 and 50 are all multiples of 2. Factor and
multiple are the same fact seen from two ends: 2 is the jump, and 4, 12, 14, 50 are
the landing spots.

Page 31 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q2 Which of his friends will he be able to meet if he jumps by 3 steps? (3 is a common
factor of the numbers 9, 21, 39, and 57.)

With jumps of 3 he meets the spider at 9, the frog at 12, Kaa at 21, Baloo at 30, the deer at
39 and the monkey at 57.

Green = Mowgli lands here (jumps of 3) · Grey = he jumps over

Mowgli Spider Bird Tiger Akela Rabbit
0 9 14 26 35 50

4 12 21 30 39 57
Ant Frog Kaa Baloo Deer Monkey

Jumping 3 at a time, Mowgli lands on 3, 6, 9, 12 … 57 — the multiples of 3.

1. Write where 3-jumps land. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57.
2. Look up each friend's number in that list.
3. Keep the ones you find. 9, 12, 21, 30, 39 and 57 are all there.

9=3×3✓

12 = 3 × 4 ✓

21 = 3 × 7 ✓

30 = 3 × 10 ✓

39 = 3 × 13 ✓

57 = 3 × 19 ✓

Why it happens: A 3-jump can only stop on a multiple of 3. To test a number quickly,
add up its digits: if the total is in the 3 times table, the number is too. For 57, 5 + 7 =
12, and 12 is a multiple of 3 — so 57 is as well.

What your book prints: The book names four of them — 9, 21, 39 and 57 — and
says 3 is a common factor of those numbers. That is true. But 12 and 30 are
multiples of 3 as well, so the frog and Baloo are also met.

Page 32 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q3 Which numbers will he touch if he jumps by 5 steps? 5 is a common factor of the
numbers ____________.

He touches 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55. Among his friends he meets Baloo at 30,
Akela at 35 and the rabbit at 50.
So the blank is filled like this:

5 is a common factor of the numbers 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55.

Green = Mowgli lands here (jumps of 5) · Grey = he jumps over

Mowgli Spider Bird Tiger Akela Rabbit
0 9 14 26 35 50

4 12 21 30 39 57
Ant Frog Kaa Baloo Deer Monkey

Jumps of 5 land only on numbers ending in 5 or 0.

Why it happens: Adding 5 again and again gives 5, 10, 15, 20 … Every one of these
ends in a 5 or a 0. So a number can be reached by 5-jumps only if its last digit is 5 or
0. Baloo's 30 ends in 0 ✓, Akela's 35 ends in 5 ✓, the rabbit's 50 ends in 0 ✓.

Check it yourself: 5 × 6 = 30, 5 × 7 = 35, 5 × 10 = 50. All three friends are reached ✓

Q4 Which numbers will he touch if he jumps by 10 steps? 10 is a common factor of the
numbers ____________.

He touches 10, 20, 30, 40 and 50. Among his friends he meets only Baloo at 30 and the rabbit
at 50.

10 is a common factor of the numbers 10, 20, 30, 40 and 50.

Page 33 of 58

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

co m
m.
Green = Mowgli lands here (jumps of 10) · Grey = he jumps over

m as e
.co a g l
se m
g l a
Mowgli Spider Bird Tiger Akela Rabbit

a
0 9 14 26 35 50

4 12 21
. om
c30 39 57
ag
Ant Frog Kaa
se m Baloo Deer Monkey

l a
ag land only on numbers ending in 0.
Jumps of 10

co m
Why it happens: Adding 10 each time only changes the tens digit. The ones digit
e m.
m l as
.co g
stays 0. So a 10-jump can land only on a number ending in 0 — 10, 20, 30, 40, 50.
m a
l a se
a g Notice the pattern: Every number reached by 10-jumps is also reached by 5-jumps

s
and by 2-jumps. That is because 10 = 2 × 5, so 2 and 5 are both factors of 10.
m a
m .co agl
l a se
g
Let Us Do (Questions 4–5)a— Page 168
Common factors of 24 and 36; common factors of 12 and 13
co m
m .
LET US DO
m ase
.co a g l
a s em 4. (a) Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No. 2 is/is not a
agl Q1
common factor of 24 and 36.

se m
com g l a
m . a
e

s 36.
Yes. 2 is a common factor of 24aand
l
a g
Jumps of 2 from 0
co m
m .
m as e
.co a g l
se m
g l a
a
0 6 12 18 24 30 36
.c
Jumping 2 at a time from 0, you land on both 24 and 36.
s e m
m a
em . co agl
g l as
a

co m
m .
m as e
.co


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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

24 ÷ 2 = 12, nothing left over ✓

36 ÷ 2 = 18, nothing left over ✓

So 2 is a common factor of 24 and 36

Why it happens: Both 24 and 36 are even numbers, so both can be shared into
equal pairs. That is the same as saying 2 divides each of them exactly.

Q2 4. (b) Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No. 3 is/is not a
common factor of 24 and 36.

Yes. 3 is a common factor of 24 and 36.

Jumps of 3 from 0

0 6 12 18 24 30 36

Jumping 3 at a time, you land on 3, 6, 9 … 24 … 36. Both targets are hit.

24 ÷ 3 = 8, nothing left over ✓

36 ÷ 3 = 12, nothing left over ✓

Why it happens: Add the digits and check. For 24, 2 + 4 = 6, and 6 is in the 3 times
table. For 36, 3 + 6 = 9, also in the 3 times table. So 3 divides both.

Q3 4. (c) Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No. 4 is/is not a
common factor of 24 and 36.

Yes. 4 is a common factor of 24 and 36.

Page 35 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Jumps of 4 from 0

0 6 12 18 24 30 36

Jumping 4 at a time: 4, 8, 12, 16, 20, 24, 28, 32, 36. Both 24 and 36 are landing spots.

24 ÷ 4 = 6, nothing left over ✓

36 ÷ 4 = 9, nothing left over ✓

Why it happens: 4 × 6 = 24 and 4 × 9 = 36. Because both numbers can be built out of
equal groups of 4, a 4-jump lands exactly on each of them.

Q4 4. (d) What other jumps can we take to reach both 24 and 36?

Jumps of 1, 6 and 12 also reach both numbers.

Jumps of 1
Jumps of 6
Jumps of 12

0 6 12 18 24 30 36

Three more jump sizes that land on both 24 and 36.

Jump of 1: 24 ÷ 1 = 24 ✓ and 36 ÷ 1 = 36 ✓

Jump of 6: 24 ÷ 6 = 4 ✓ and 36 ÷ 6 = 6 ✓

Jump of 12: 24 ÷ 12 = 2 ✓ and 36 ÷ 12 = 3 ✓

Page 36 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Some jump sizes do not work:

Jump of 5: 24 ÷ 5 leaves 4 over ✗

Jump of 8: 36 ÷ 8 leaves 4 over ✗

Jump of 9: 24 ÷ 9 leaves 6 over ✗

Why it happens: A jump size works only if it divides both numbers exactly. 8 divides
24 but not 36, so it is a factor of 24 alone — not a common factor.

Q5 4. (e) How many common factors can you find for 24 and 36? List them.

There are six common factors: 1, 2, 3, 4, 6 and 12.

1. List all the factors of 24. 1, 2, 3, 4, 6, 8, 12, 24.
2. List all the factors of 36. 1, 2, 3, 4, 6, 9, 12, 18, 36.
3. Tick the numbers that are in both lists. 1, 2, 3, 4, 6, 12.
4. Count them. Six common factors.

FACTORS OF 24 1, 2, 3, 4, 6, 8, 12, 24

FACTORS OF 36 1, 2, 3, 4, 6, 9, 12, 18, 36

COMMON FACTORS 1, 2, 3, 4, 6, 12

Why it happens: Unlike common multiples, common factors always run out. No
common factor can be bigger than the smaller number, so for 24 and 36 the search
stops at 24. Here the biggest common factor is 12.

Notice: The common factors 1, 2, 3, 4, 6 and 12 are exactly the factors of 12 — the
biggest common factor. That happens with every pair of numbers.

Q6 4. (f) What about jumping by 1 step each time to reach both 24 and 36?

Yes, a jump of 1 works — and it works for every number.

Page 37 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Jumping 1 at a time: 1, 2, 3, 4, 5 … 24 … 36

24 ÷ 1 = 24 ✓ and 36 ÷ 1 = 36 ✓

Why it happens: Jumping 1 step at a time means you touch every number on the
number line. So you must pass through 24 and through 36. This is why 1 is a
common factor of every pair of numbers.

The book's note says: The number itself and 1 are always factors of any number. So the
shortest list of common factors any two numbers can have is just 1.

Q7 5. What are the common factors of 12 and 13?

The only common factor of 12 and 13 is 1.

1. Factors of 12: 1, 2, 3, 4, 6, 12.
2. Factors of 13: 1, 13 — because 13 is a prime number.
3. Compare the two lists. The only number in both is 1.

Factors of 12 → 1, 2, 3, 4, 6, 12

Factors of 13 → 1, 13

Common factor = 1

Why it happens: 13 has only two factors, 1 and 13. Since 13 does not divide 12 (12 ÷
13 is not a whole number), the only factor they can share is 1.

Did you know? 12 and 13 follow one another on the number line. Two numbers that
follow one another always have 1 as their only common factor.

Let Us Do (Questions 6–7) — Page 169

Page 38 of 58

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

Which numbers do jumps of 4 reach? Common factors of number pairs
co m
em.
m as
LET US DO DISCUSS IN CLASS

.co a g l
s m which of the following numbers can be reached by jumps of 4 steps?
eFind
gl a6.
a
Q1

com
e m . ag
g l as
a
0 10 16 27 36 48

co m
Page 169, Question 6 — the number line with 0, 10, 16, 27, 36 and 48 marked on it.
em.
m l as
m .co a g
l a se 4 is the common factor of the numbers ____________.

ag
s
m a
m .co
Jumps of 4 reach 16, 36 and 48. They do not reach 10 or 27.
agl
l a se
a g
4 is the common factor of the numbers 16, 36 and 48.

co m
m .
m as e
.co
Jumps of 4 from 0
a g l
se m
g l a
a
se m
0 10 16
com
27 36 48
g l a
m . a
ase
The red dots are the landing spots for jumps of 4. They fall on 16, 36 and 48, but skip past 10 and 27.

agl
m
NUMBER DIVIDE BY 4 REACHED?
cNoo
.
em
com as
10 10 ÷ 4 = 2 with 2 left over

.16 a g l
e m
as
16 ÷ 4 = 4 exactly Yes

agl c
.
27 27 ÷ 4 = 6 with 3 left over No

s e m
m a
.co agl
36 36 ÷ 4 = 9 exactly Yes

se m
48
g l a
48 ÷ 4 = 12 exactly Yes

a

co m
m .
m ase
.co


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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: A 4-jump lands on 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 — the 4
times table. 10 sits between 8 and 12, and 27 sits between 24 and 28, so the jumps
go straight over them. Also, 27 is an odd number, and a 4-jump can never land on an
odd number.

Q2 7. (a) 12 and 16

The common factors of 12 and 16 are 1, 2, 4.

FACTORS OF 12 1, 2, 3, 4, 6, 12

FACTORS OF 16 1, 2, 4, 8, 16

COMMON FACTORS 1, 2, 4

1. Write every factor of 12.
2. Write every factor of 16.
3. Pick the numbers that are in both lists. They are 1, 2, 4.

Why it happens: Both numbers are built from 4s: 12 = 4 × 3 and 16 = 4 × 4. So 4
divides both, and so do 4's own factors, 1 and 2. But 3 divides only 12, and 8 divides
only 16.

Q3 7. (b) 8 and 12

The common factors of 8 and 12 are 1, 2, 4.

FACTORS OF 8 1, 2, 4, 8

FACTORS OF 12 1, 2, 3, 4, 6, 12

COMMON FACTORS 1, 2, 4

1. Write every factor of 8.
2. Write every factor of 12.
3. Pick the numbers that are in both lists. They are 1, 2, 4.

Page 40 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 8 = 4 × 2 and 12 = 4 × 3. So 4 is the biggest common factor, and the
common factors are exactly the factors of 4 — that is 1, 2 and 4.

Q4 7. (c) 4 and 16

The common factors of 4 and 16 are 1, 2, 4.

FACTORS OF 4 1, 2, 4

FACTORS OF 16 1, 2, 4, 8, 16

COMMON FACTORS 1, 2, 4

1. Write every factor of 4.
2. Write every factor of 16.
3. Pick the numbers that are in both lists. They are 1, 2, 4.

Why it happens: 4 is itself a factor of 16, because 16 = 4 × 4. When the smaller
number divides the bigger one, the common factors are simply all the factors of the
smaller number.

Q5 7. (d) 2 and 9

The common factors of 2 and 9 are 1.

FACTORS OF 2 1, 2

FACTORS OF 9 1, 3, 9

COMMON FACTORS 1

1. Write every factor of 2.
2. Write every factor of 9.
3. Pick the numbers that are in both lists. They are 1.

Page 41 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 2 is even and 9 is odd, so 2 cannot divide 9. And 9's other factors, 3
and 9, are too big to divide 2. Only 1 is left.

Notice: When 1 is the only common factor, the two numbers share nothing else at
all.

Q6 7. (e) 3 and 5

The common factors of 3 and 5 are 1.

FACTORS OF 3 1, 3

FACTORS OF 5 1, 5

COMMON FACTORS 1

1. Write every factor of 3.
2. Write every factor of 5.
3. Pick the numbers that are in both lists. They are 1.

Why it happens: 3 and 5 are both prime numbers — each has only two factors, itself
and 1. Since 3 does not divide 5, the only number they share is 1.

Q7 7. (f) 12 and 15

The common factors of 12 and 15 are 1, 3.

FACTORS OF 12 1, 2, 3, 4, 6, 12

FACTORS OF 15 1, 3, 5, 15

COMMON FACTORS 1, 3

1. Write every factor of 12.
2. Write every factor of 15.
3. Pick the numbers that are in both lists. They are 1, 3.

Page 42 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: Both numbers are in the 3 times table: 12 = 3 × 4 and 15 = 3 × 5. So
3 is a common factor. But 12 is even and 15 is odd, so 2 is not.

Q8 7. (f) 20 and 5

The common factors of 20 and 5 are 1, 5.

FACTORS OF 20 1, 2, 4, 5, 10, 20

FACTORS OF 5 1, 5

COMMON FACTORS 1, 5

1. Write every factor of 20.
2. Write every factor of 5.
3. Pick the numbers that are in both lists. They are 1, 5.

Why it happens: 5 divides 20 exactly, because 20 = 5 × 4. So the common factors are
all the factors of 5, which are 1 and 5.

A note on the book: This list also prints the label (f) twice — once for "12 and 15"
and again for "20 and 5". There are nine pairs in all, and all nine are answered here
in the printed order.

Q9 7. (g) 9 and 21

The common factors of 9 and 21 are 1, 3.

FACTORS OF 9 1, 3, 9

FACTORS OF 21 1, 3, 7, 21

COMMON FACTORS 1, 3

1. Write every factor of 9.
2. Write every factor of 21.

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

3. Pick the numbers that are in both lists. They are 1, 3.
co m
em.
m l as
.co a g
Why it happens: 9 = 3 × 3 and 21 = 3 × 7. The only number they both contain is 3, so

se m
the common factors are 1 and 3.
g l a
a

co m
Q10 7. (h) 6 and 27
e m . ag
g l as
ANSWER a
The common factors of 6 and 27 are 1, 3.
co m
em.
m l as
.co g
FACTORS OF 6 1, 2, 3, 6

m a
l a se
g
FACTORS OF 27 1, 3, 9, 27

a
COMMON FACTORS 1, 3

m a s
m .co agl
se
1. Write every factor of 6.

g l a
a
2. Write every factor of 27.
3. Pick the numbers that are in both lists. They are 1, 3.

co m
m .
e
Why it happens: 6 = 3 × 2 and 27 = 3 × 9. They share the 3. But 6 is even and 27 is
m l as
.co g
odd, so 2 is not shared.
m a
l a se
ag
What do you notice about the common factors of different pairs of numbers.
se m
com a
Q11
Discuss in class.
. a g l
m
ase
agl
Sample answer: Every pair of numbers has at least one common factor — the number 1. Some

co m
.
pairs have nothing else. The list of common factors is always short, and it always stops; it can

e m
as
never go past the smaller of the two numbers.
m l
m .co a g
l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

KIND OF PAIR EXAMPLES FROM THIS COMMON FACTORS
EXERCISE

The smaller number divides the 4 and 16; 20 and 5 All the factors of the smaller
bigger one number

They share a factor bigger than 1 12 and 16; 12 and 15; 9 and 21; 6 1 and that shared factor (and its
and 27 factors)

They share nothing but 1 2 and 9; 3 and 5 Only 1

Four things to notice:

1. 1 is a common factor of every pair. A jump of 1 lands on every number.
2. The list of common factors always ends — unlike common multiples, which go on for ever.
3. No common factor is bigger than the smaller number. For 9 and 21, nothing above 9 can
be a common factor.
4. The whole list is made of the factors of the biggest common factor. For 12 and 16 the
biggest is 4, and the list 1, 2, 4 is exactly the factors of 4.

Why it happens: A common factor has to fit inside both numbers. The smaller
number sets the limit, because nothing larger than a number can divide it.

Let Us Do (Question 8: True or False) — Page 169
State whether the following statements are true (T) or false (F).

LET US DO

Q1 8. (a) Factors of even numbers must be even.

False (F).
An even number can easily have odd factors.

Factors of 6 → 1, 2, 3, 6 — 1 and 3 are odd

Factors of 10 → 1, 2, 5, 10 — 1 and 5 are odd

Factors of 12 → 1, 2, 3, 4, 6, 12

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: 6 counters can be set out as 3 rows of 2. The 3 rows make 3 a
factor, and 3 is odd. In fact 1 is a factor of every number, and 1 is odd — so no
number can have only even factors.

Q2 8. (b) Multiples of odd numbers cannot be even.

False (F).
Jump 3 steps at a time and you land on 3, 6, 9, 12, 15, 18 … Every second landing spot is even.

3 × 2 = 6 (even)

3 × 4 = 12 (even)
5 × 2 = 10 (even)

7 × 6 = 42 (even)

Why it happens: An odd number multiplied by an even number always gives an
even answer. So the multiples of an odd number go odd, even, odd, even, odd, even
… turn by turn.

Check on the number line: The frog jumping 3 lands on 3, 6, 9, 12. Two of those
four spots are even.

Q3 8. (c) Factors of odd numbers cannot be even.

True (T).

Factors of 9 → 1, 3, 9 — all odd

Factors of 15 → 1, 3, 5, 15 — all odd

Factors of 21 → 1, 3, 7, 21 — all odd

Page 46 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Why it happens: If an even number were a factor of some number, that number
could be split into equal groups of 2 — which would make it even. An odd number
cannot be split into equal pairs; one is always left over. So no even number can ever
divide an odd number exactly.

Try it: Take 15 counters and try to make pairs. You get 7 pairs and 1 counter left
over. So 2 is not a factor of 15 — and neither is 4, 6, 8 or any other even number.

Q4 8. (d) One of the common multiples of two consecutive numbers is their product.

True (T).
Consecutive numbers are numbers that follow one after the other, like 4 and 5, or 9 and 10.

4 and 5 → 4 × 5 = 20. And 20 ÷ 4 = 5 ✓, 20 ÷ 5 = 4 ✓

9 and 10 → 9 × 10 = 90. And 90 ÷ 9 = 10 ✓, 90 ÷ 10 = 9 ✓

7 and 8 → 7 × 8 = 56 ✓

Why it happens: If you multiply two numbers together, the answer can be split into
equal groups of the first number and into equal groups of the second. So the
product is always a common multiple — of any two numbers, not only consecutive
ones.

Careful: The product is a common multiple, not always the smallest one. For 4 and 6
the product is 24, but the smallest common multiple is 12. For consecutive numbers,
though, the product really is the smallest one.

Q5 8. (e) The only common factor of any two consecutive numbers is 1.

True (T).

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

PAIR FACTORS OF THE FIRST FACTORS OF THE SECOND COMMON

8 and 9 1, 2, 4, 8 1, 3, 9 1

12 and 13 1, 2, 3, 4, 6, 12 1, 13 1

14 and 15 1, 2, 7, 14 1, 3, 5, 15 1

Why it happens: Think of jumps again. Suppose a jump of 3 lands on 14. The very
next landing spot is 17, not 15 — because after landing, the animal must travel a full
3 steps before it can land again. Two numbers that are only 1 step apart can never
both be landing spots for a jump bigger than 1. So the only jump size that reaches
both is 1.

Q6 8. (f) 0 cannot be a factor of any number.

True (T).

0×1=0
0×5=0

0 × 100 = 0

Whatever you multiply 0 by, the answer is always 0

Why it happens: A factor is a number you can multiply by something to get your
number. But 0 multiplied by anything gives 0 — never 12, never 25, never any other
number. Jumping 0 steps at a time means you never move off 0. So 0 is a factor of no
number at all.

Related fact: Dividing by 0 is not allowed in mathematics. You cannot share 12
sweets among 0 children.

Let Us Do (Questions 9–10) — Page 169

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

Hunting days; choosing a jump size to meet or avoid a friend
co m
e m.
m as
LET US DO

.co a g l
s m Khan, the tiger, goes hunting every 3rd day. Bagheera, the panther, goes
eSher
gl a9.
a
Q1
hunting every 5th day. If both of them start on the same day, on which days will
they be hunting together?

co m
m . ag
l a se
ag30, day 45, day 60 … that is, every 15th day.
They hunt together on day 15, day

co m
Sher Khan hunts every 3rd day
em.
m l as
.co g
Bagheera hunts every 5th day
m a
l a se
a g
m a s
m .co 30 agl
ase
0 15 45 60

agl
The two rows of dots meet only on 15, 30, 45 and 60 — the common multiples of 3 and 5.

co m
.
1. Write Sher Khan's days. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …

e m
m as
2. Write Bagheera's days. 5, 10, 15, 20, 25, 30 …

.co a g l
m
3. Find the days in both lists. 15, 30, 45, 60 …

l a se
ag Common multiples of 3 and 5 = 3 × 5 = 15, then 30, 45, 60, 75 …
se m
com g l a
m. a
ase
Why it happens: 3 and 5 share no factor except 1. When that is so, the first day they
agl
meet is simply 3 × 5 = 15. After that the whole pattern repeats, so they meet again
every 15 days.

co m
m .
as e
om Both are whole numbers ✓ g l
Check it yourself: 15 ÷ 3 = 5 (Sher Khan's 5th hunt) and 15 ÷ 5 = 3 (Bagheera's 3rd

m .chunt). a
l a se
ag
.c
s e m
m a
e m . co agl
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a

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q2 10. (a) In the trail shown earlier, Sher Khan's house is on number 25 and that of
Baloo the bear is on number 30. Mowgli wants to meet his friend Baloo the bear but
wants to avoid Sher Khan's house. How long (in steps) could each jump be?

His jump could be 2, 3, 6, 10, 15 or 30 steps.
The jump has to do two things at once: reach 30, and miss 25.

1. Find the jump sizes that reach 30. These are the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
2. Find the jump sizes that would land on 25. These are the factors of 25: 1, 5, 25.
3. Cross out any jump size that is in both lists. Cross out 1 and 5.
4. What is left is the answer. 2, 3, 6, 10, 15, 30.

JUMP REACHES 30? LANDS ON 25? SAFE FOR MOWGLI?

1 Yes Yes No — he walks right past Sher Khan

2 Yes (2 × 15) No (25 is odd) Yes

3 Yes (3 × 10) No Yes

5 Yes (5 × 6) Yes (5 × 5) No

6 Yes (6 × 5) No Yes

10 Yes (10 × 3) No Yes

15 Yes (15 × 2) No Yes

30 Yes (30 × 1) No Yes

Why it happens: A jump size lands on a number only if it is a factor of that number.
So Mowgli needs a factor of 30 that is not a factor of 25. The only factors 25 and 30
share are 1 and 5 — and those two are exactly the ones he must avoid.

Smallest safe jump: 2 steps. Mowgli lands on 2, 4, 6 … 24, 26, 28, 30. He hops
straight over 25 and arrives at Baloo's house.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q3 10. (b) What number of jumps (in steps) he could choose so that he can meet both
Kaa, the snake, at 21 and Akela, the wolf, at 35?

He should jump 7 steps at a time. (A jump of 1 step also works, but it is the slow way.)

1. The jump must reach 21, so it must be a factor of 21: 1, 3, 7, 21.
2. The jump must also reach 35, so it must be a factor of 35: 1, 5, 7, 35.
3. Take the numbers in both lists. 1 and 7.
4. Choose the useful one. 7 steps.

Factors of 21 → 1, 3, 7, 21

Factors of 35 → 1, 5, 7, 35

Common factors = 1 and 7

With 7-step jumps he lands on:

7, 14, 21, 28, 35, 42, 49, 56

Kaa is met on the 3rd jump, Akela on the 5th

Why it happens: To visit two houses with equal jumps, the jump size must divide
both house numbers exactly. That is exactly what a common factor is. Here 21 = 7 ×
3 and 35 = 7 × 5, so 7 fits into both.

Check it yourself: Try 3 steps. You reach 21, but then 24, 27, 30, 33, 36 — you jump
over 35. Try 5 steps. You reach 35, but you land on 20 and 25, skipping 21.

Let Us Do (Question 11: Sorting) — Page 170

Page 51 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Sort 90, 45, 84, 22, 66, 56, 38, 78, 25, 30, 62, 95, 75, 40 and 55

LET US DO

Q1 11. Sort the following numbers into those that are — (a) divisible by 2 only

22, 38, 66, 78, 62, 84 and 56 are divisible by 2 only.
A number is divisible by 2 if it is even — that is, if its last digit is 0, 2, 4, 6 or 8. "Divisible by 2
only" means it is even but not divisible by 5, so it must not end in 0.

NUMBER LAST DIGIT DIVISIBLE BY 2? DIVISIBLE BY 5?

22 2 Yes No

38 8 Yes No

66 6 Yes No

78 8 Yes No

62 2 Yes No

84 4 Yes No

56 6 Yes No

Why it happens: Jumping 2 at a time from 0 lands you on every even number. None
of these seven numbers ends in 0 or 5, so 5-jumps miss them all.

Q2 11. (b) divisible by 5 only

75, 45, 25, 95 and 55 are divisible by 5 only.
A number is divisible by 5 if its last digit is 5 or 0. "Divisible by 5 only" means it must not also be
even — so it has to end in 5.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

75 ÷ 5 = 15 ✓ but 75 is odd, so 2 does not divide it

45 ÷ 5 = 9 ✓

25 ÷ 5 = 5 ✓

95 ÷ 5 = 19 ✓

55 ÷ 5 = 11 ✓

Why it happens: All five numbers end in 5. Numbers ending in 5 are always odd, so
they can never be divisible by 2 or by 10.

Q3 11. (c) divisible by 10 only

There are none. This box stays empty.
Not one of the fifteen numbers can go here — and in fact no number ever can.

10 = 2 × 5

So every multiple of 10 is also a multiple of 2 and of 5

90 ÷ 10 = 9, and also 90 ÷ 2 = 45, 90 ÷ 5 = 18

Why it happens: A jump of 10 is the same as five jumps of 2, or two jumps of 5. So
wherever a 10-jump lands, a 2-jump and a 5-jump have already been. A number can
never be divisible by 10 alone.

This is the point of the question. An empty box is a real answer. It shows that 2 and
5 are hidden inside 10, so the three circles of the diagram can never be separate.

Q4 11. (d) divisible by 2, 5, and 10

90, 30 and 40 are divisible by 2, by 5 and by 10.

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Class 5 Maths Chapter 13 Animal Jumps
a g l AglaSem · NCERT Solutions

co m
m.
NUMBER ÷2 ÷5 ÷ 10

m a9 s e
90
.co
45 18
a g l
se m
g l a
a
30 15 6 3

40 20 8 4

com
m . ag
l a se
Why it happens: All three numbers end in 0. A number ending in 0 is even, so 2
agso 5 divides it; and ending in 0 is exactly the test for
divides it; it also ends in 0 or 5,
10. The one digit 0 settles all three tests at once.

co m
e m.
m l as
.co g
Tip: Look only at the last digit. Ends in 0 → divisible by 2, 5 and 10. Ends in 5 →

em a
s
divisible by 5 only. Ends in 2, 4, 6 or 8 → divisible by 2 only. Ends in 1, 3, 7 or 9 →
a
gl none of the three.
a
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Q5 Complete the diagram on page 170 by writing each number in the right place.

90 22 38 30 75

45 66 78 62 40

84 56 25 95 55

Numbers divisible Numbers divisible
only by 2 only by 5

Numbers divisible by
2, 5 and 10

Numbers divisible
only
by 10

Page 170 — the fifteen number cards and the blank sorting diagram to be filled in.

Here is the finished diagram, with all fifteen numbers placed.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

divisible by 2 only divisible by 5 only

22, 38, 66 75, 45, 25
78, 62, 84 95, 55
56
90
30
40 by 2, 5 and 10

None

divisible by 10 only
All fifteen numbers sorted. The bottom part, for numbers divisible by 10 only, stays empty.

PART OF THE DIAGRAM NUMBERS HOW MANY

Divisible only by 2 22, 38, 66, 78, 62, 84, 56 7

Divisible only by 5 75, 45, 25, 95, 55 5

Divisible by 2, 5 and 10 90, 30, 40 3

Divisible only by 10 None 0

Check the count: 7 + 5 + 3 + 0 = 15

There were 15 numbers to sort ✓

Why it happens: Sorting like this is really sorting by the last digit. Ends in 0 → the
middle, shared part. Ends in 5 → the "5 only" part. Ends in 2, 4, 6 or 8 → the "2 only"
part.

Page 56 of 58

Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Check it yourself: Read the numbers off the page one by one — 90, 22, 38, 30, 75,
45, 66, 78, 62, 40, 84, 56, 25, 95, 55 — and tick each one as you place it. Every
number should be used exactly once.

Chapter at a glance
A jump size is a factor. A landing spot is a multiple. If you start at 0 and jump 4 steps
every time, you land on 4, 8, 12, 16, 20 … Every number you land on is a multiple of 4. And 4
is a factor of every one of those numbers, because 4 divides each of them exactly, with
nothing left over. This one picture is the whole chapter: jump size = factor, landing spot =
multiple.
Factors are small, multiples are big. A number has only a few factors, and they are never
bigger than the number itself. 12 has six factors: 1, 2, 3, 4, 6 and 12. But 12 has endless
multiples: 12, 24, 36, 48, 60 … which go on for ever. If you mix the two words up, ask
yourself: am I jumping, or am I landing?
An array shows the factors. Arrange 12 counters in a neat rectangle. You can make 3 rows
of 4, or 2 rows of 6, or 1 row of 12. Each rectangle gives you a pair of factors: 3 and 4, 2 and
6, 1 and 12. Together they give all six factors of 12.
Prime numbers make only one rectangle. Try to arrange 13 counters in a rectangle. The
only way is one long row of 13. So 13 has just two factors, 1 and 13. Numbers like 13 and 37
are called prime numbers.
Common multiples — where two animals land together. The frog jumps 3 (3, 6, 9, 12 …)
and the rabbit jumps 4 (4, 8, 12 …). They meet at 12, then 24, then 36. These shared landing
spots are the common multiples of 3 and 4. There are always endless common multiples,
and every one of them is a multiple of the smallest one.
Common factors — jump sizes that reach both numbers. Which jump sizes take you
exactly to both 24 and 36? Jumps of 1, 2, 3, 4, 6 and 12 all work. These are the common
factors of 24 and 36. There are only a few of them, and 1 is a common factor of every pair
of numbers.
Two useful shortcuts. If one number is a multiple of the other (like 3 and 6), then the
smaller number's list already contains the bigger one — so the first common multiple is the
bigger number itself. And if two numbers share nothing except 1 (like 3 and 4), their first
common multiple is simply 3 × 4 = 12.
Divisibility, quickly. A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8. It is divisible by 5 if
it ends in 0 or 5. It is divisible by 10 only if it ends in 0. So every number that is divisible by
10 is automatically divisible by both 2 and 5 — which is why a box for numbers divisible only
by 10 must stay empty.

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Class 5 Maths Chapter 13 Animal Jumps AglaSem · NCERT Solutions

Quick revision

WORD WHAT IT MEANS WHERE IT EXAMPLE
APPEARS

Factor A number that divides another number Page 164, the box 4 is a factor of 28,
exactly, leaving nothing over game because 28 = 4 × 7

Multiple The number you get when you multiply Page 164 28, 36, 48 and 72 are
— the spot you land on multiples of 4

Array Objects set out in equal rows and Page 164, arrays for 3 rows of 4 counters
columns, in a rectangle 15 and 12 show 3 × 4 = 12

Prime number A number with exactly two factors — 1 Page 165, the red 13 and 37 are prime
and itself note numbers

Number line A straight line with the numbers marked Pages 165–166 0, 1, 2, 3 … with arcs
in order, used to show jumps drawn over it

Common A number that is a multiple of two (or Page 165, rabbit and 12 is a common multiple
multiple more) numbers frog of 3 and 4

Common factor A number that divides two (or more) Page 168, the pink 2 is a common factor of 4,
numbers exactly banner 12, 14 and 50

Divisible Divides exactly, with remainder 0 Page 170, Question 90 is divisible by 2, by 5
11 and by 10

Consecutive Numbers that follow one after the other Page 169, Question 7 and 8; 24 and 25
numbers 8

Even number A number that ends in 0, 2, 4, 6 or 8 Page 169, Question 26, 30, 50
8

Odd number A number that ends in 1, 3, 5, 7 or 9 Page 169, Question 9, 21, 57
8

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