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# If 15!/3^m is an integer, what is the greatest possible value of m?

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Re: If 15!/3^m is an integer, what is the greatest possible value of m? [#permalink]
Bunuel wrote:
If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

Breaking down the primes of 3 within 15! we have:

3

6 = 3 x 2

9 = 3^2

12 = 2^2 x 3

15 = 3 x 5

We see that there are 6 factors of 3 in 15!, and thus the maximum value of m is 6.

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Re: If 15!/3^m is an integer, what is the greatest possible value of m? [#permalink]
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