Problem #WSP-000378

Problem

Prove that each natural number $n\ge 2$ 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 $q_1,\dots ,q_l$ are prime, then $s=l$ and after reordering we have $q_1=p_1,\dots ,q_s=p_s$. This is the fundamental theorem of arithmetic.