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# What is the smallest positive integer n for which 324 is a

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Director
Joined: 17 Oct 2005
Posts: 869
What is the smallest positive integer n for which 324 is a  [#permalink]

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30 Nov 2005, 10:38
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What is the smallest positive integer n for which 324 is a factor of 6^n?

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Senior Manager
Joined: 11 Nov 2005
Posts: 298
Location: London

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30 Nov 2005, 10:45
N=4

N =1, 6
N=2, 36
N=3, 216
N=4, 1296

324 IS FACTOR OF 1296
Director
Joined: 03 Sep 2006
Posts: 767

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26 May 2007, 18:41
joemama142000 wrote:
What is the smallest positive integer n for which 324 is a factor of 6^n?

324 = (2^2)*(3^4) = (6^2)*(9^1)

Any number to be completely divisible by 324 should have at least 6^2 and then should have a number divisible by 9. If it only in terms of powers of 6 then the number divisble by 9 would be 36 ( 6^2)

Therefore, (6*6*6*6)/(6^2)*(9^1) = 4.

Q.E.D
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Re: What is the smallest positive integer n for which 324 is a  [#permalink]

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10 Apr 2019, 09:26
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Re: What is the smallest positive integer n for which 324 is a   [#permalink] 10 Apr 2019, 09:26
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