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What is the total number of zeroes in $n!$?

I do not want to know the number of trailing zeroes in $n!$.

Let us take an example to understand what I want to know.

$7! = 5040$. The number of trailing zero in $7!$ is $1$. But the total number of zeroes in $7!$ is $2$.

I would like to know if there is any formula that gives me directly the total number of zeros in $n!$.

Can you help me derive one?

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    To the best of my knowledge, there is no known method (apart from calculating the base 10 representation and counting the zeros) of calculating the number of non-trailing zeros. [This might be useful](https://oeis.org/A137581).2012-12-29
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    Related: http://math.stackexchange.com/questions/142126/how-many-zeroes-are-in-1002012-12-29
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    @Sultan In the english language, by convention, there is no space between a sentence and its ending punctuation, whether that's a period, a question mark, or an exclamation mark. There should also be no space before a colon, semicolon, or comma. The only punctuation mark that sometimes needs to be preceded by a space is a dash. I have edited the post making these changes.2012-12-29

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