What is the greatest common factor of 60 and 84?

Answer 1

First, list the factors of each number.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

Now, list all the common factors -- the factors that appear in both lists: 1, 2, 3, 4, 6, and 12.

The largest factor on that list, 12, is the GCF.

That is why they called it "The Greatest Common Factors".

Alternate Method

You can also determine the greatest common factor from the prime factors.

The prime factors of 60 are 2, 2, 3, and 5.

The prime factors of 84 are 2, 2, 3, and 7.

The prime factors they have in common are 2, 2, and 3, so the greatest common factor is 2 x 2 x 3 = 12.

60 = 2^2 x 3 x 5

84 = 2^2 x 3 x 7

Therefore, since the gcf is a combination of the highest power of primes that are found in both factorisations,

gcf = 2^2 x 3 = 12