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Prime Factor Question (GMAT Prep Exam)

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Newbie | Next Rank: 10 Posts
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Joined: Mon May 07, 2007 3:28 pm
Location: Pasadena, CA

Prime Factor Question (GMAT Prep Exam)

by abbyyip » Tue Jul 24, 2007 8:07 pm
Is there a simple method of solving this?

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

2
3
5
7
11







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The answer is 7
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Junior | Next Rank: 30 Posts
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Location: india

by manred » Tue Jul 24, 2007 8:29 pm
4^17 - 2^28
= 2^34 - 2^28
= 2^28 (2^6 - 1)
=2^28 (64 - 1)
=2^28 * (63)
=2^28 * (9 * 7)
=2^28 * 3^2 * 7

So the prime factors of (4^17 - 2^28 ) are 2, 3, 7

Hence the greatest prime factor is 7.
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Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Mon May 07, 2007 3:28 pm
Location: Pasadena, CA

by abbyyip » Thu Jul 26, 2007 3:27 pm
wow thanks so much!
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