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# What is the highest prime factor in the expression

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

40% (01:20) correct 60% (01:22) wrong based on 5 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
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1897 [1] , given: 397

Re: What is the highest prime factor in the expression [#permalink]  20 Feb 2017, 12:31
1
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Expert's post
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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