Find the highest power of 5 in (100)!

Explanation

To find the highest power of 5 in \(100!\), we can use the formula for determining the highest power of a prime \(p\) in \(n!\):

\[ \text{Highest power of } p \text{ in } n! = \left\lfloor \frac{n}{p} \right\rfloor + \left\lfloor \frac{n}{p^2} \right\rfloor + \left\lfloor \frac{n}{p^3} \right\rfloor + \ldots \]

where \(\left\lfloor x \right\rfloor\) denotes the greatest integer less than or equal to \(x\).

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