## Question on factorial.

Forum for the GRE subject test in mathematics.
Murali830
Posts: 1
Joined: Wed Sep 12, 2012 10:40 am

### Question on factorial.

what is the highest power of 3 which divides 99999!

vonLipwig
Posts: 51
Joined: Sat Mar 17, 2012 9:58 am

### Re: Question on factorial.

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?

DDswife
Posts: 118
Joined: Thu Aug 14, 2014 5:29 pm

### Re: Question on factorial.

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 + ...

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