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What is the greatest value of a positive integer n such that

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New post 10 Jan 2014, 01:58
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What is the greatest value of a positive integer n such that \(3^n\) is a factor of \(18^1^2\)?

A) 17
B) 24
C) 31
D) 33
E) 47
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Re: What is the greatest value of a positive integer n such that  [#permalink]

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New post 10 Jan 2014, 02:04
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New post 10 Jan 2014, 02:09
18 = 2*3*3 = 2*3^2 Therefore this term to the power of 12 equals: 2^12 * (3^2)^12

This equals 2^12 *3^24 since we can multiple the exponents of base 3.

The only possible answer is 24 which is also the greatest answer. Thus, the answer is B.

Note that if there were answers such as 6 and 12, but 24 (the greatest value) would not be among the answers, we would pick the greatest value. Thus, between 6 and 12 we would pick 12 since 3^12 would be one multiple of the overall term.

However, note that in the given case no other answer would match. None of the answers except B would even qualify as a lower possible value.
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Re: What is the greatest value of a positive integer n such that  [#permalink]

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New post 14 Aug 2015, 13:13
Please tag Divisibility/Factors/multiples
BabySmurf wrote:
What is the greatest value of a positive integer n such that \(3^n\) is a factor of \(18^1^2\)?

A) 17
B) 24
C) 31
D) 33
E) 47

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Re: What is the greatest value of a positive integer n such that  [#permalink]

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New post 27 Jun 2017, 15:34
BabySmurf wrote:
What is the greatest value of a positive integer n such that \(3^n\) is a factor of \(18^1^2\)?

A) 17
B) 24
C) 31
D) 33
E) 47


Simple- the most practical way we can break down 18^12 is 9^12 x 2^12 = 3^24 x 2^12

Thus
"B"
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Re: What is the greatest value of a positive integer n such that   [#permalink] 27 Jun 2017, 15:34
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