Find the number of zeros at the end of 100!.

Explanation

To find the number of zeros at the end of \(100!\), we need to determine how many times \(10\) is a factor in \(100!\). Since \(10\) can be expressed as \(2 \times 5\), we need to find the minimum of the number of factors of \(2\) and \(5\) in \(100!\).

### Step 1: Calculate the exponent of \(2\) in \(100!\)

The formula to find the exponent of a prime \(p\) in \(n!\) is given by:

\[
\sum_{k=1}^{\infty} \left\lfloor \frac{n}{p^k} \right\rfloor
...