Factors and multiples - 5

Finding factors of a given number

In the earlier post, we learnt about divisibility tests of various numbers. We are going to use it to find out the factors of a given number. In this post, we are going to learn about finding various factors of a given number. 

We will call this method as the factor pair method. Let's start with an example. 

Writing down the factor pairs of the number 18. 

18	=	1 x 18	The actual factor pairs
	=	2 x 9
	=	3 x 6
	=	6 x 3	Same as 3 x 6
	=	9 x 2	Same as 2 x 9
	=	18 x 1	Same as 1 x 18

∴ The factors of the number 18 are 1, 2, 3, 6, 9 and 18.

Steps to find the factor pairs:

1.   As we have already discussed, 1 and the number itself are the factors of any given number. Therefore the pair of 1 and the number itself becomes the first pair of factors.  

2.   If the given number is an even number, then 2 is one of the factors. Divide the given number by 2, the quotient obtained is the other number of the factor pair.

          e.g.

          18 ÷ 2 = 9

              ∴ The factors of 18 are 2 and 9. Hence The next factor pair is 2 x 9.

3.   Using the divisibility tests, we can see that 18 is divisible by 3.

              ∴ 18 ÷ 3 = 6

              ∴ The next factor pair is 3 x 6

4.   Similarly we observe that 18 is divisible by 6 and 9 as well.

∴ 18 ÷ 6 = 3

∴ The factor pair can be 6 x 3

But it is same as 3 x 6.

∴ 18 ÷ 9 = 2

∴ The factor pair can be 9 x 2

But it is same as 9 x 2.

Let's consider another example. Writing down the factor pairs of the number 48.

48	=	1 x 48	The actual factor pairs
	=	2 x 24
	=	3 x 16
	=	4 x 12
	=	6 x 8
	=	8 x 6	Same as 6 x 8
	=	12 x 4	Same as 4 x 12
	=	16 x 3	Same as 3 x 16
	=	24 x 2	Same as 24 x 2

∴ The factors of the number 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Practice time:

List the factor pairs of the following numbers:

54

63

75

87

99

128

144

Answers