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# What is the greatest prime factor of 2^100 - 2^96? A. 2

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SVP
Joined: 14 Dec 2004
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What is the greatest prime factor of 2^100 - 2^96? A. 2  [#permalink]

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31 Dec 2005, 05:23
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What is the greatest prime factor of 2^100 - 2^96?

A. 2
B. 3
C. 5
D. 7
E. 11

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Director
Joined: 17 Dec 2005
Posts: 544

Kudos [?]: 40 [0], given: 0

Location: Germany

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31 Dec 2005, 05:33
2^100 - 2^96=

(2^4)*(2^96) - 2^96= 2^96(2^4 - 1)

The greatest prime factor of 2^96 is 2

2^4 - 1= 15, so the prime factor are 3 and 5

It is C, I think

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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

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Location: Singapore

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09 Jan 2006, 01:33
2^100 - 2^96 = 2^96 (2^4 - 1) = 15 (2^96) = 3*5*2^96

Ans C

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CEO
Joined: 20 Nov 2005
Posts: 2892

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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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09 Jan 2006, 02:27
C

2^100 - 2^96= 2^96(2^4 - 1) = (2^96) * 15

So prime factors are 2,3,5
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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VP
Joined: 20 Sep 2005
Posts: 1016

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10 Jan 2006, 15:13
5 in 5 seconds...hope that I don't get such questions in the actual GMAT..which would probably mean that I screwed up big time....

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10 Jan 2006, 15:13
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