The number of zeros at the end of 2007! Is ________ .

Explanation

To find the number of zeros at the end of \(2007!\), we need to determine how many times \(10\) can be formed as a factor in the factorial. Since \(10\) is the product of \(2\) and \(5\), we will find the maximum powers of \(2\) and \(5\) in \(2007!\) and take the minimum of these two values.

### Step 1: Find the maximum power of \(5\) in \(2007!\)

We use the formula for the maximum power of a prime \(p\) in \(n!\):
\[ \text{Maximum power of } p = \left\lfloor \frac{n}{p} \right\rfloor + \left\lfloor \frac{n}{p^2} \right\rfloor + \left\lfloor \frac{n}{p^3} \right\rfloor + \ldots \]
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