(a) We denote the product of the first 20 natural numbers by 20! and call this 20 factorial.

What is the highest power of 5 which is a divisor of 20 factorial? Just how many factors does 20! have altogether?

b) Show that the highest power of $k$ that divides 500!, where $k$ is an integer and $k^{(t + 1)} > 500 > k^t $ is ,

$$[500/k] + [500/k^2] + ... + [500/k^t].$$

where the square brackets are used to denote the integer part of the number inside.

(c) How many factors does $n!$ have?