# Factoring Monomials

We know that the Fundamental Theorem of Arithmetic states that any whole number can be written uniquely as a product of prime factors . What about factoring monomials?

The " prime factorization " of a monomial is its expression as a product of prime numbers , single variables, and (possibly) a $-1$ .

Example:

Find the prime factorization of $-27{p}^{2}q{r}^{5}$ .

$27$ can be written as $3\cdot 3\cdot 3$ . Then just write the powers out the long way, and multiply by $-1$ .

$-27{p}^{2}q{r}^{5}=-1\cdot 3\cdot 3\cdot 3\cdot p\cdot p\cdot q\cdot r\cdot r\cdot r\cdot r\cdot r$