Tuesday, April 9, 2019

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

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