The exponent of 7 in 100!, is

Options

A. 14
B. 15
C. 16
D. none of these

Explanation

To find the exponent of 7 in \(100!\), we can use the formula for the exponent of a prime \(p\) in \(n!\):

\[ \text{Exponent of } p \text{ in } n! = \sum_{k=1}^{\infty} \left\lfloor \frac{n}{p^k} \right\rfloor \]

In this case, \(n = 100\) and \(p = 7\). We will calculate the sum until \(p^k\) exceeds \(n\).

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