# Zeroes After a Factorial

Let $$f(n,k)$$ be the number of zeroes at the end of $$n!$$ in base $$k$$.

Let $$g(r)=f(r,2)+f(r,3)+f(r,4)+...+f(r,r)$$

Find $$g(100)$$

----- Examples -----

$$f(100,10)=24$$

$$f(53, 7)=8$$

$$f(5,16)=0$$

$$g(7)=12$$

$$g(25)=136$$

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