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

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What is the greatest prime factor of 2^100 - 2^96? A. 2  [#permalink] New post 26 Aug 2004, 21:14
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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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 [#permalink] New post 26 Aug 2004, 21:36
2^100 - 2^96 = 2^96(2^4-1) = 2^96(15) = 2^96(3)(5)

So the greatest prime number is 5
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 [#permalink] New post 27 Aug 2004, 00:27
I got answer C too.

However I did solve it differently, and would like to know if my approach is possible.

2^10 - 2^6 = 1024 - 64 = 960

5 is the greatest prime number to divide 960.

Like I said, I am not sure if my approach is correct. I hope someone can give me some feedback.

Regards,

Alex
  [#permalink] 27 Aug 2004, 00:27
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What is the greatest prime factor of 2^100 - 2^96? A. 2

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