Year 8 Interactive Maths - Second Edition

Highest Common Factor

The highest common factor (HCF) of two or more numbers is the largest number that is a factor of all of the given numbers.

Example 21

Find the highest common factor of:

a.  16 and 24
b.  28 and 42

Solution:

Consider the highest common factor of 16 and 24 again.

The common factors are 1, 2, 4 and 8.  So, the highest common factor is 8.

In general:

To find the highest common factor of two (or more) numbers, make prime factors of the numbers and identify the common prime factors.  Then the highest common factor is the product of the common prime factors.

Example 22

Find the highest common factor of 60 and 150.

Solution:

The prime factorisation of 60 is:

The prime factorisation of 150 is:

Note:

The highest common factor can also be obtained by a trial and error method.

For example, the highest common factor of 40 and 45 is 5 because 5 is the largest number which divides into both 40 and 45 exactly.

Similarly, the highest common factor of 27 and 36 is 9 because 9 is the largest number which divides into both 27 and 36 exactly.

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