GMAT prep, prime factors

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LFalken: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed May 13, 2009 5:40 am; Location: MN; Thanked: 1 times; GMAT Score:580

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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Source: Beat The GMAT — Problem Solving | Mon Sep 07, 2009 9:40 am

rish: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Fri Jul 24, 2009 11:47 am; Thanked: 5 times

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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