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

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Manager
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What is the greatest prime factor of 2^100 - 2^96? A. 2 B. 3 [#permalink] New post 10 Oct 2008, 08:51
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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Re: prime number [#permalink] New post 10 Oct 2008, 08:54
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
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Re: prime number [#permalink] New post 10 Oct 2008, 08:56
Jcpenny wrote:
What is the greatest prime factor of 2^100 - 2^96?

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



my answer is C

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

therefore the greatest prime factor is 5.
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Re: prime number [#permalink] New post 10 Oct 2008, 10:03
same here !

:)
Re: prime number   [#permalink] 10 Oct 2008, 10:03
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What is the greatest prime factor of 2^100 - 2^96? A. 2 B. 3

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