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

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

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New post 13 Mar 2019, 00:45
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A
B
C
D
E

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  15% (low)

Question Stats:

72% (00:45) correct 28% (01:29) wrong based on 81 sessions

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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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New post 13 Mar 2019, 00:50
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


15/3 = 5

15/9 = 1

Total number of 3's in 15! = 6.

C is the correct answer.

For more , check out club's material .
https://gmatclub.com/forum/math-number- ... 88376.html
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If 15!/3^m is an integer, what is the greatest possible value of m?  [#permalink]

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New post 10 Apr 2019, 08:11
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What is the question really asking here?

It's simply asking: For the quotient to be an integer, we need the same number of factors of 3 in the numerator as we need in the denominator. So our task here is to find how many factors of 3 are in the numerator, which means the denominator could have just as many to maintain that the quotient is an integer.

So \(\frac{15!}{3^m}\) is really \(\frac{15*14*13*12*11*10*9.....}{3*3*3*3.....}\)

The question asks for the max number of 3's in the denominator. We already established, for the quotient to be an integer, we need to figure out how many 3's are in the numerator!

So simply count the factors of 3. That's 3, 6, 9, 12, 15... So that's 5 factors!! Nope, 9 has 2 factors of 3, so 6 factors.
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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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New post 13 Apr 2019, 18:35
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.

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

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Re: If 15!/3^m is an integer, what is the greatest possible   [#permalink] 02 May 2019, 01:27
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