Given two numbers a and b, the greatest common divisor can be found by prime factorising each number and then grouping together the common ones.


Example 1:

Find the highest common factor of a and b, where a = 168 and b = 294.

Solution:

a = 2 x 2 x 2 x 3 x 7

b= 2 x 3 x 7 x 7

So the grouping the common ones we have:

hcf (highest common factor) = 2 x 3 x 7 = 42


Example 2:

Find the highest common factor of a and b, where a = 15750and b = 12375.

Solution:

a = 2 x 3 x 3 x 5 x 5 x 5 x 7

b= 3 x 3 x 5 x 5 x 5 x 11

So the hcf = 3 x 3 x 5 x 5 x 5 = 1125