Highest Common Factor Worksheets 31

What are factors?

The two numbers that we multiply together to get a multiple are called factors.

Factor x Factor = Multiple

4 x 7 = 28

What are common factors?

When you list the factors of two or more numbers (or multiples), sometimes you can see some factors are in all the lists of factors. These factors which appear in all the lists of factors are called common factors.

What is Highest Common Factor (HCF)?

The largest common factor of a list of common factors is called the Highest Common Factor. In short we call it HCF.

What is Greatest Common Factor (GCM)?

Highest common factor (HCF) is also known as the Greatest Common Factor (GCM).

Follow the example below to find the highest common factor (HCF) or the greatest common factor (GCF) of a number pair.

Find the highest common factor (HCF) of 24 and 32

Example 1:

Step 1:

Find the factors of 24

1, 2, 3, 4, 6, 8, 12, 24

Step 2:

Find the factors of 32

1, 2, 4, 8, 16, 32

Step 3:

Group the common factors

1, 2, 4, 8

Step 4:

Find the highest factor of all the common factors

8 is the highest factor of all the common factors of 24 and 32

Therefore 8 is the highest common factor of 24 and 32

Example 2:

Find the highest factor, which is common to both numbers that each number is divisible by.

This factor is the highest common factor of the number pair.

24

32

÷

÷

8

8

=

3

4

Step 1:

Find the factors of 15

1, 3, 5, 15

Step 2:

Find the factors of 30

1, 2, 3, 5, 6, 10, 15, 30

Step 3:

Find the factors of 105

1, 3, 5, 7, 15, 21, 35, 105

Step 4:

Group the common factors

1, 3, 5, 15

Step 5:

Find the highest factor of all the common factors

15 is the highest factor of all the common factors of 15, 30 and 105