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What is the highest prime factor in the expression

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Intern
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Joined: 19 Feb 2017
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What is the highest prime factor in the expression [#permalink] New post 20 Feb 2017, 09:57
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Question Stats:

100% (02:00) correct 0% (00:00) wrong based on 1 sessions
What is the highest prime factor in the expression

\(\frac{3^{18} - 3^{12}}{3^5}\)

A) 3

B) 7

C) 11

D) 13

E) 19
[Reveal] Spoiler: OA

Last edited by Carcass on 12 Dec 2017, 11:55, edited 3 times in total.
Edited by Carcass
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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: What is the highest prime factor in the expression [#permalink] New post 20 Feb 2017, 12:31
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Explanation

Take the expression

\(\frac{3^1^8 - 3^1^2}{3^5}\) or \(3^1^2\frac{3^6 - 1}{3^5}\)= \(3^7 \times 728\).

Clearly the highest prime factor of the expression \(\frac{3^1^8 - 3^1^2}{3^5}\) also is the highest prime factor of 728.

Try \(\frac{728}{19}\). Doesn't work!

Try \(\frac{728}{13}\). Works!

Hence D is the right answer.
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Re: What is the highest prime factor in the expression   [#permalink] 20 Feb 2017, 12:31
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What is the highest prime factor in the expression

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