Greatest Common Factor

The largest among the common factors of two or more numbers is called their greatest common factor (GCF). The greatest common factor is also called the greatest common divisor.

The Greatest Common Factor is also called the Highest Common Factor (HCF).

Example :

Find the GCF of 48 and 60

Solution:

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Common factors of 48 and 60 are 1,2,3,4,6,12.
The greatest factor is 12. So the GCF of 48 and 60 is 12.

Repetitive Division

Using the lists to find the GCF can be slow and tedious. A faster method would be to use repetitive division to find the highest common factors.

Example :

The GCF of 48 and 60 is obtained by multiplying the numbers in the left column:
4 × 3 = 12

The following video gives more examples of finding the greatest common factor of two numbers.

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