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The highest common factor (abbreviated to HCF) is the largest number that goes into two or more subject-numbers. For example, the common factors of 40 and 16 are 2, 4 and 8.

The HCF of 40 and 16 is therefore 8. This is the largest number that 'goes into' both numbers.

Example one

Find the HCF of 12 and 20.

The factors of 12 are: 1, 2, 3, 4, 6, 12.

The factors of 20 are: 1, 2, 4, 5, 10, 20.

The HCF is therefore 4, as this is the largest number that goes into both 12 and 20.

Example two

Find the HCF of 42 and 24.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The HCF of 42 and 24 is therefore 6.

Example three

Find the HCF of 12 and 24.

The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The HCF of 12 and 24 is therefore 12.

Example four

Find the HCF of 12, 24, and 39.

The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The factors of 39 are 1, 3, 13, 39.

The HCF of 12, 24 and 39 is therefore 3.