Greatest prime factor?

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Fri May 08, 2009 8:44 am

What is the greatest prime factor of 2^100 - 2^96?
A. 2
B. 3
C. 5
D. 7
E. 11

How is it 5? Can someone explain an easy way to solve this problem?

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Source: Beat The GMAT — Problem Solving | Fri May 08, 2009 8:44 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Fri May 08, 2009 8:47 am

2^100 - 2^96

Pull out a factor of 2^96. This will leave you with:

2^96(2^4 - 1)
2^96(16 - 1)
2^96(15)
2^96(3*5)

The prime factors are 2, 3, and 5. 5 is the greatest.

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Fri May 08, 2009 9:42 am

ohh!! knew this way...anyways tx for refreshing

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