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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}