(b) Show that the highest power of $k$ that divides 500!, where $k$ is an integer and $k^{(t + 1)} > 500 > k^t$ is
$$\left[500/k\right] + \left[500/k^2\right] + \ldots + \left[500/k^t\right]\;,$$
(c) How many factors does $n!$ have?