Euclid's lemma

In number theory, Euclid's lemma, named after the ancient Greek geometer and number theorist Euclid of Alexandria, states that if a prime number p is a divisor of the product of two integers, ab, then either p is a divisor of a or p is a divisor of b (or both).

Euclid's lemma is used in the proof of the unique factorization theorem, which states that a number cannot have more than one prime factorization.