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What is the greatest prime factor of 2^100 - 2^96? A. 2 B. 3

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Manager
Joined: 10 Oct 2008
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What is the greatest prime factor of 2^100 - 2^96? A. 2 B. 3 [#permalink]

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10 Oct 2008, 09:51
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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
SVP
Joined: 05 Jul 2006
Posts: 1512
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10 Oct 2008, 09:54
Jcpenny wrote:
What is the greatest prime factor of 2^100 - 2^96?

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

2^96(2^4 - 1) = 2^96*15 , 5 is the answer

C
Manager
Joined: 15 Apr 2008
Posts: 165
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10 Oct 2008, 09:56
Jcpenny wrote:
What is the greatest prime factor of 2^100 - 2^96?

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

2^100-2^96= 2^96 (2^4-2^1)
=2^96*15=2^96*3*5

therefore the greatest prime factor is 5.
Manager
Joined: 27 Sep 2008
Posts: 76
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10 Oct 2008, 11:03
same here !

Re: prime number   [#permalink] 10 Oct 2008, 11:03
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