Trailing Zeros of n! (Legendre's Formula)

The number of trailing zeros of $n!$ in base $b$ is the minimum, over the prime powers $p^e \| b$, of $\lfloor v_p(n!)/e \rfloor$, where Legendre's formula gives $v_p(n!) = \sum_{i\ge 1} \lfloor n/p^i \rfloor$.