The largest n N, for which 7^n divides 101!, is :

Question

The largest $n\in N$, for which ${7}^{n}$ divides $101!$, is :

Accepted Answer

The exponent of the prime $7$ in $101!$ is:
$$\left\lfloor \frac{101}{7} \right\rfloor + \left\lfloor \frac{101}{49} \right\rfloor = 14 + 2 = 16$$

Solutions · 1