Hallar la mayor potencia de $2$ que divida a $(2^4)!$.

Nota:

Los números $2,4,8,16,\ldots$ son potencias de $2$, esto es, son de la forma $2^k,\,k=1,2,3,\ldots$
Para cualquier número natural $n\geq 1$, se define $n!$ como

$n!=1\times 2\times 3\times\cdots\times n.$

Find the greatest power of $2$ that divides $(2^4)!$.

Note:

The numbers $2,4,8,16,\ldots$ are powers of $2$, that is, they have the form $2^k,\,k=1,2,3,\ldots$
For any natural number $n\geq 1$, $n!$ is defined as
$n!=1\times 2\times 3\times\cdots\times n.$