Prime factor of big numbers?

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imadummy: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed May 21, 2008 6:55 am

by imadummy » Thu Jul 31, 2008 9:18 am

What is the largest prime factor of 4^17 – 2^28?

1. 7

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Source: Beat The GMAT — Problem Solving | Thu Jul 31, 2008 9:18 am

VP_RedSoxFan: GMAT Instructor; Posts: 85; Joined: Thu May 01, 2008 12:56 pm; Location: Salt Lake City, UT; Thanked: 24 times; GMAT Score:750+

by VP_RedSoxFan » Thu Jul 31, 2008 9:20 am

I think this one has been answered before, but I'll help out anyway:

The first thing I'd do is turn the 2^28 into 4^14, giving you 4^17 - 4^14.

Then, I'd factor our the 4^14 leaving me with

4^14(4^3 - 1)

I know the prime factors represented by 4^14 will just be 28 2's. So as long as I get something more than a 2 as a prime factor of 4^3 -1 then that will be the answer. 4^3 - 1 = 63 whose prime factors are 3, 3, 7. So the prime factorization of this difference is 28 2's, 3, 3, and 7, the largest, of course, is 7.

Ryan S.
| GMAT Instructor |
Elite GMAT Preparation and Admissions Consulting
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Gouman: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Jun 17, 2008 10:06 am; Location: Los Angeles

by Gouman » Tue Jun 23, 2009 12:08 am

Nice response. I like that.

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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

by BlindVision » Tue Jun 23, 2009 12:39 am

Understandable response! Good job!

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