highest power

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tushar7
Posts:101
Joined:Tue Dec 07, 2010 3:23 pm
highest power

Unread post by tushar7 » Thu Jan 06, 2011 1:50 am

what is the highest power of $3$ in $35!$
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HandaramTheGreat
Posts:135
Joined:Thu Dec 09, 2010 12:10 pm

Re: highest power

Unread post by HandaramTheGreat » Thu Jan 06, 2011 12:58 pm

15
$\lfloor \frac{35}{3} \rfloor + \lfloor \frac{35}{3^2} \rfloor + \lfloor \frac{35}{3^3} \rfloor$
there're 11 numbers less than or equal to 35 which are divisible by 3(that means which has 3 as a factor), 3 numbers which are divisible by 9(the numbers which has 2 threes as factor... we've already counted 1three in the previous term) and there's also 1 number which has 3 threes...
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