# 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.

$\begin{array}{l}-27{p}^{2}q{r}^{5}=-1\cdot {3}\cdot 3\cdot 3\cdot {p}\cdot {p}\cdot q\cdot {r}\cdot {r}\cdot {r}\cdot r\cdot r\\ 15{p}^{3}{r}^{3}={3}\cdot 5\cdot {p}\cdot {p}\cdot p\cdot {r}\cdot {r}\cdot {r}\end{array}$

Common factors are shown in red. Their product is:

$3\cdot p\cdot p\cdot r\cdot r\cdot r$

So, the GCF is $3{p}^{2}{r}^{3}$ .