I need to find that the number of the 0's at the end of the number is odd or even in a factorial.
For example:
$0! = 1$ (Even)
$5! = 120 $ (Odd)
$18! = 6402373705728000 $ (Odd)
Dou you have any idea about this problem?
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Martin Sleziak
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g3d
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look at answers of this question – achille hui Apr 27 '14 at 06:55
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I want the # of 0's at the end of the result. – g3d Apr 27 '14 at 06:58
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That will be much easier, just count the number of $5$ in your $n!$ using De Polignac's formula. i.e $$\sum\limits_{k=1}^{\left\lfloor \frac{\log n}{\log 5}\right\rfloor} \left\lfloor \frac{n}{5^k} \right\rfloor$$. – achille hui Apr 27 '14 at 07:01
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Thanks. I have another question, from $1$ to $n$ how many numbers have even # of 0's? $(0!,1!, .... , n!)$ – g3d Apr 27 '14 at 07:17