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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.
Note:
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.
Key Terms
highest common factor, HCF
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