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What is the greatest prim factor of (4)^17-(2)^28?

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nk2120
 Post subject: What is the greatest prim factor of (4)^17-(2)^28?
 Post Posted: Sun Jan 04, 2009 5:10 pm 
Anybody? Thanks!
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Misha
 Post subject:
 Post Posted: Sun Jan 04, 2009 8:27 pm 
Quote:
What is the greatest prim factor of (4)^17-(2)^28?


First, simplify to obtain common factors:
4^17 = (2^2)^17 = 2^34

Thus question becomes:
2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 (64-1) = 2^28 (63) = 2^28 (9*7) = 2^28 (3*3*7)

Looks like 2, 3, 7 are the prime factors, and thus appears that 7 is the GCF-prime.
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RonPurewal
 Post subject:
 Post Posted: Fri Jan 09, 2009 6:50 am 
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ManhattanGMAT Staff


Posts: 7146
please, PLEASE search first. this is one of the most-posted problems on this whole board.

http://www.manhattangmat.com/forums/post862.html

http://www.manhattangmat.com/forums/wha ... t2924.html

http://www.manhattangmat.com/forums/wha ... -t411.html

http://www.manhattangmat.com/forums/gre ... t2410.html

http://www.manhattangmat.com/forums/gma ... t2761.html

and that's just the top 5 from ONE SEARCH (search keywords: 17 28 prime factor).

please don't be lazy, people. search first. thanks.
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