Theorem (All Numbers Have Prime Divisors)

Every number $n\in\mathbb{N}$ where $n>1$ has a prime divisor.

Theorem (All Numbers have Prime Factorization)

Every natural number $n\in\mathbb{N}$ such that $n>1$ can be written as a product of prime numbers.

Theorem (If a Prime divides ab it divides one of a or b)

If $p$ is a prime, and $p|ab$ then we have that either $p|a$ or $p|b$.