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Question on factorial.

Posted: Wed Sep 12, 2012 10:43 am
by Murali830
what is the highest power of 3 which divides 99999!

Re: Question on factorial.

Posted: Wed Sep 12, 2012 9:19 pm
by vonLipwig
The number 99999! is the product of all the integers between 1 and 99999. How many of those numbers are multiples of 3? How many are multiples of 9? Of 27?

Re: Question on factorial.

Posted: Sun Aug 17, 2014 7:19 pm
by DDswife
Every 3 multiple of 3 you have a multiple of 3^2. Every 3 multiple of 3^2, we have a multiple of 3^3, and so on.

So, divide by 3, and the quotient again, and again, disregarding the remainders if they are not 0

Then add all the quotients you go.

99999/3 = 33333 multiples pf 3
33333/3 = 11111 multiples of 3^2
11111/3 ~ 3703 multiples of 3^3
Etc

Then you add 33333+ 11111 + 3703 + ...