Fact of Factorials

Number Theory Level 4

Let $$f(n) : \mathbb{Z}^+ \to \mathbb{Z}$$ be a function which gives the number of trailing zeros in $$n!$$.

Then find,

$\lim_{n\to \infty} \frac{f(n)}{n}$

Details and Assumptions

• For example, if $$n=3$$, then $$3! = 6$$, so $$f(3) = 0$$; if $$n=7$$, then $$7! = 5040$$, so $$f(7) = 1$$
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