By Legendre’s formula, the exponent of a prime $p$ in $N!$ is ${\sum }_{i\ge 1}\lfloor \frac{N}{p^i}\rfloor$.

For $p=7$, $N=101$: $\lfloor \frac{101}{7}\rfloor +\lfloor \frac{101}{49}\rfloor +\lfloor \frac{101}{343}\rfloor +\dots =14+2+0+\dots =16$.