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 Discussion Response Post to:
1000!
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![[Post New]](/templates/default/images/icon_minipost_new.gif) 6 Mar 2008 18:23:40 IST
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highest power of a prime "p" in factorial n:( [t]=greatest integer function)
is [n/p] + [n/p^2] +.... ( continue till u get 0)
generally in 1000!, there is lower power of 5 than power of 2 ( u want highest 10ans ) if p<q and u get 5^p*2^q from my abv relation, your answer will obviously be p, u can leave out the extra 2,s they dont contribute to zero, if u calculate for 5 u will get 249., try for power of 2, u will more than that...this is a method only to find zeros at the end, but u cannot find no. of zeros in between using this method.
for proof, refer TMH or "Higher algebra" by hall and knight...Hope this helped
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