 Specifically, if a prime number divides "L", then it must divide at least one factor of "L".Conversely, if a number "w" is coprime to each of a series of numbers "a"1, "a"2, ..., "a""n", then "w" is also coprime to their product, "a"1 × "a"2 × ... × "a""n".Euclid's lemma suffices to prove that every number has a unique factorization into prime numbers.