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GMAT prep, prime factors

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Senior | Next Rank: 100 Posts
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GMAT prep, prime factors

by LFalken » Mon Sep 07, 2009 9:40 am
question off my latest GMAT prep test that I cannot find the solution to, if anyone would show me I would appreciate it greatly. Thanks


What is the greatest prime factor of 4^17-2^28?

a)2
b)3
c)5
d)7 (correct answer)
e)11
LFAL
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Senior | Next Rank: 100 Posts
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by rish » Mon Sep 07, 2009 10:15 am
4^17 - 2^28
=(2^2)^17 - 2^28
=2^34 - 2^28
=2^28(2^6 - 1)
=2^28(2^3 - 1)(2^3 + 1)
=2^28(7)(9)

Thus, the greatest prime factor is 7
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