Prove that each natural number \(n\geq 2\) can be uniquely written as a product of prime factors. More precisely, there are prime numbers \(p_1,\dots,p_s\) such that \(n = p_1\dots p_s\). Moreover, if \(n = q_1\dots q_l\) where \(q_1,\dots,q_l\), then \(s=l\) and after reordering we have \(q_1 = p_1,\dots,q_s=p_s\). This is the fundamental theorem of arithmetic.