Common Factors

Factors are the numbers you multiply together to get another number

These are counting numbers that divide a whole number exacty without living a remainder

Factors are also divisors of a number.

To get them easily think of families of a number for example what numbers can be multiplied to give the answer 12?

These are;

1. 1 x 12
2. 2 x 6
3. 3 x 4

Therefore, 1, 2, 3, 4, 6 and 12 are the factors or divisors of 12 (They are like families of 12).

 

Example 1

What are the factors of 42?

Solution

1 x 42

2 x 21

3 x14

6 x 7

Therefore, 1,2,3,6,7,14,21 and 42 are the factors of 42.

 

 

Example 2

List all factors of 45

Solution

1 x 4

3 x 15

5 x 9

Therefore, 1,3,5,9,15 and 45 are factors of 45.

 

Example 3

What are the divisors of 21?

Solution

1 x 21

3 x 7

Therefore, 1,3,7 and 21 are the (factors) of 21

Factors that are common to two or more numbers are said to be common factors.

When you find the factors of two or more numbers, and then find some factors are the same ("common"), then they are the "common factors".

For example,   4 = 1x4 = 2x2

                      6 = 1x6 = 2x3

Therefore Factors of 4 are 1,2 and 4.

Therefore Factors of 6 are 1,2,3 and 6.

So, the common factors of 4 and 6 are 1 and 2

 

 

Find the common factors of 10 and 30.

Solution

10 = 1x10 = 2x5

30 = 1x30 = 2x15 = 5x6 = 3x10

So, the common factors of 10 and 30 are 1, 2, 5 and 10.

Watch this video to learn more!

The common factors of 15, 30 and 105

Factors of 15 are 1, 3, 5 and 15

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105

 

The factors that are common to all three numbers are 1, 3, 5 and 15

In other words, the common factors of 15, 30 and 105 are 1, 3, 5 and 15