2023 Fermat Problem 20

If n is a positive integer, the symbol n! (which is read "n factorial") represents the product of the integers from 1 to n, inclusive. For example, 5! = (1)(2)(3)(4)(5) or 5! = 120, which ends with exactly 1 zero. For how many integers m, with 1 \le m \le 30, is it possible to find a value of n so that n! ends with exactly m zeros?

\textbf{(A)}\ 30\quad \textbf{(B)}\ 27\quad \textbf{(C)}\ 28\quad \textbf{(D)}\ 24\quad \textbf{(E)}\ 25

If there are no answer choices shown, enter a numerical answer.

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