@Labib Rashid
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Oh! I think I missed the word 'algorithm'. But I don't think the OP meant algorithm literally [It's tagged with number theory]. Despite that, you're right. That algorithm will go on forever in the natural sense. I just posted that because I think that looks cool :)

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TopNewestThe highest power of p that divides n! is

\(\displaystyle\sum_{i=1}^{j}\left \lfloor \frac{n}{p^i} \right \rfloor\)

,where j is the biggest integer, for which \(p^j<n\)

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I think it should be \(p^j \leq n\)

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True. But you could save yourself from the trouble by just putting \[\displaystyle \sum_{i=1}^\infty \lfloor\frac{n}{p^i}\rfloor\].

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