NCERT Book Class 8 Maths Chapter 12 Factorisation

FACTORISATION 145

CHAPTER

Factorisation
12
12.1 Introduction
12.1.1 Factors of natural numbers
You will remember what you learnt about factors in Class VI. Let us take a natural number,
say 30, and write it as a product of other natural numbers, say
30 = 2 × 15 We know that 30 can also be written as
= 3 × 10 = 5 × 6 30 = 1 × 30
Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30. Thus, 1 and 30 are also factors of 30.
You will notice that 1 is a factor of any
Of these, 2, 3 and 5 are the prime factors of 30 (Why?)
number. For example, 101 = 1 × 101.
A number written as a product of prime factors is said to However, when we write a number as a
be in the prime factor form; for example, 30 written as product of factors, we shall not write 1 as
2 × 3 × 5 is in the prime factor form. a factor, unless it is specially required.
The prime factor form of 70 is 2 × 5 × 7.
The prime factor form of 90 is 2 × 3 × 3 × 5, and so on.
Similarly, we can express algebraic expressions as products of their factors. This is
what we shall learn to do in this chapter.
12.1.2 Factors of algebraic expressions
We have seen in Class VII that in algebraic expressions, terms are formed as products of
factors. For example, in the algebraic expression 5xy + 3x the term 5xy has been formed
by the factors 5, x and y, i.e.,
5xy = 5 × x × y Note 1 is a factor of 5xy, since
Observe that the factors 5, x and y of 5xy cannot further 5xy = 1 × 5 × x × y
be expressed as a product of factors. We may say that 5, In fact, 1 is a factor of every term. As
x and y are ‘prime’ factors of 5xy. In algebraic expressions, in the case of natural numbers, unless
we use the word ‘irreducible’ in place of ‘prime’. We say that it is specially required, we do not show
5 × x × y is the irreducible form of 5xy. Note 5 × (xy) is not 1 as a separate factor of any term.
an irreducible form of 5xy, since the factor xy can be further
expressed as a product of x and y, i.e., xy = x × y.