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PREP

by dunkin77 » Mon Jun 18, 2007 3:22 pm
What is the greatest prime factor of 2^100 - 2^96?

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


CAN ANYONE HELP?
Last edited by dunkin77 on Tue Jun 19, 2007 3:18 am, edited 2 times in total.
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Re: PREP

by jayhawk2001 » Mon Jun 18, 2007 4:19 pm
dunkin77 wrote:What is the greatest prime factor of 2100 - 296?

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


CAN ANYONE HELP?
Hmm, 2100-296 = 1804 = 4 * 451 = 4 * 11 * 41

I'm getting 41 as the greatest prime factor...
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by moneyman » Tue Jun 19, 2007 1:06 am
Here is my approach..

2100-296 is 1804

1804 is 11*164 and since the greatest prime from the given options is asked..I think the answer would be E..Am I right??
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by dunkin77 » Tue Jun 19, 2007 3:19 am
Sorry, I think I wrote it wrong. :oops:

It's 2^100 - 2^96 .
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by gabriel » Tue Jun 19, 2007 5:17 am
dunkin77 wrote:Sorry, I think I wrote it wrong. :oops:

It's 2^100 - 2^96 .

.. so that wuld be 2^96(2^4-1) = 2^96*15 .. so the prime factors fro this number are 2,3,5 ... and the highest is 5 ..
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by dunkin77 » Tue Jun 19, 2007 5:58 am
you're right - thank you:)
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