Greatest Common Factor of Monomials

To find the greatest common factor of two monomials, first find the prime factorization of each monomial, including all the variables (and a 1 factor if necessary).

Then take the product of all common factors.

Example:

Find the GCF of:

–27p2qr5

and

15p3r3

First, find the prime factorization of each monomial.

–27p2qr5 = –1 · 3 · 3 · 3 · p · p · q · r · r · r · r · r

15p3r3 = 3 · 5 · p · p · p · r · r · r

Common factors are shown in red. Their product is:

3 · p · p · r · r · r

So, the GCF is 3p2r3.