Greatest Common Factor (GCF) of Monomials

Monomial
A monomial is a polynomial with only one term.

Greatest Common Factor of Monomials
In order to find the Greatest Common Factor of a monomial, (1) first you must take each monomial and write it's prime factorization, (2) next, identify the common factors, (3) finally, multiply the common factors together.

Problem #1
Find the greatest common factor:

9x

2

, 6x

3

Step 1
Find the prime factorization of each monomial

9x

2

= 3 · 3 · x · x

6x

3

= 2 · 3 · x · x · x

Step 2
Identify the common factors:
3, x and x

Step 3
Multiply the common factors together

3 · x · x

= 3x

2

Answer:

The Greatest Common Factor is 3x

2

Problem #2
Find the greatest common factor:

4, 6x

2

Step 1
Find the prime factorization of each monomial

4

= 2 · 2 

6x

2

= 2 · 3 · x · x 

Step 2
Identify the common factors:
2

Step 3
Multiply the common factors together

2

Answer:

The only common factor is 2, therefore 2 is the Greatest Common Factor.