Past exam of the options I course of the University of Oxford / 2011 / C / 1 / a / ii

The fundamental theorem of arithmetic says that every integer $n>1$ is a product of prime numbers, uniquely up to reordering. Equivalently, $n={\prod }_p{p}^{a_p}$ for a unique family of nonnegative integer exponents, only finitely many of which are nonzero.