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 $-1$.

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