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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.

First, find the prime factorization of each monomial.

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

Common factors are shown in red. Their product is:

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