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# what is the largest integer value of x that makes 30!/3^x an

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Intern
Joined: 05 Aug 2008
Posts: 13
what is the largest integer value of x that makes 30!/3^x an [#permalink]

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19 Aug 2008, 07:33
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

what is the largest integer value of x that makes 30!/3^x an integer?

10

12

14

16

18
Senior Manager
Joined: 06 Apr 2008
Posts: 428
Re: keeping them rolling [#permalink]

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19 Aug 2008, 07:37
pattydread wrote:
what is the largest integer value of x that makes 30!/3^x an integer?

10

12

14

16

18

30! is multiple of 30, 27, 24, 21, 18, 15, 12, 9, 6, 3 = $$3*3^3*3*3*3^2*3*3*3^2*3*3 = 3 ^ 14$$

Therefore answer is 14
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: keeping them rolling [#permalink]

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19 Aug 2008, 13:21
pattydread wrote:
what is the largest integer value of x that makes 30!/3^x an integer?

10

12

14

16

18

$$30/3 + 30/3^2(nearest integer) + 30/3^3 (nearest integer)$$
= 10+3 +1=14
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Director
Joined: 23 May 2008
Posts: 799
Re: keeping them rolling [#permalink]

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19 Aug 2008, 14:30
can someone please add an explanation with more detail?
Senior Manager
Joined: 16 Jul 2008
Posts: 288
Schools: INSEAD Dec'10
Re: keeping them rolling [#permalink]

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20 Aug 2008, 00:35
bigtreezl wrote:
can someone please add an explanation with more detail?

This is the same problem as this one:
7-t69074

So, we have to count the 3's in 30!. This is done like x2suresh did: 10 numbers have at least one 3, 3 numbers have one additional 3 each, and one number (27) has yet one more 3. Which makes 14.
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Last edited by Nerdboy on 20 Aug 2008, 22:00, edited 1 time in total.
Director
Joined: 23 May 2008
Posts: 799
Re: keeping them rolling [#permalink]

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20 Aug 2008, 09:08
ok..i get it now..thanks nerdboy
Re: keeping them rolling   [#permalink] 20 Aug 2008, 09:08
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# what is the largest integer value of x that makes 30!/3^x an

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