Find the exponent of 3 in 100!

Explanation

To find the exponent of 3 in 100!, we will use the formula for the exponent of a prime \( p \) in \( n! \):

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

In this case, \( n = 100 \) and \( p = 3 \).

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