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
