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:

27 p 2 q r 5

and

15 p 3 r 3

First, find the prime factorization of each monomial.

27 p 2 q r 5 =1333ppqrrrrr 15 p 3 r 3 =35ppprrr

Common factors are shown in red. Their product is:

3pprrr

So, the GCF is 3 p 2 r 3 .