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}*qr*^{5}.

27 can be written as 3 · 3 · 3. Then just write the powers out the long way, and multiply by –1.

–27*p*^{2}*qr*^{5} = –1 · 3 · 3 · 3 · *p* · *p *· *q* · *r *· *r* · *r *· *r* · *r*