Euclid's lemma

Let \(a\) and \(b\) be any integers. If \(p\) is prime and if \(p\) divides \(ab\), then either \(p\) divides \(a\) or \(p\) divides \(b\).
Let \(a_1, a_2, \ldots, a_n\) be integers. If \(p\) is a prime number and if \(p \mid a_1a_2{\ldots}a_n\), then \(p \mid a_i\) for some \(i\) with \(1 \le i \le n\).