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

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GMAT 5/18
 Post subject: What is the greatest prime factor of 4^17 - 2^28?
 Post Posted: Sun May 13, 2007 12:23 am 
Source: Gmat Prep, mba.com, Test II

Didn't know where to start on this one. Guessed incorrectly on the exam. :(

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

a. 2
b. 3
c. 5
d. 7
e. 11

Thanks!
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vanD
 Post subject:
 Post Posted: Sun May 13, 2007 2:47 pm 
D

First reduce the exp till you have the same bases... 2^34-2^28=2^34(2^6-1)==> x(64-1)=x(63)==> x(3^2*7)

Hence 7..

hth
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GMAT 5/18
 Post subject:
 Post Posted: Sun May 13, 2007 3:43 pm 
vanD,

Thanks for helping out.

During the practise test I took, I managed to get to 2^34 - 2^28 (as you have shown).

However, I do not understand how you get to your next step of 2^34(2^6-1). Could you (or anyone else) please elaborate on this further?

Thanks a lot!
Top 
Guest
 Post subject:
 Post Posted: Sun May 13, 2007 6:02 pm 
5/18, typo... it is 2^28 not 2^34.
I got this by common factoring 2^28 between 2^34 and 2^28 so 2^28(2^6-1) since 28+6=34
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GMAT 5/18
 Post subject:
 Post Posted: Sun May 13, 2007 7:22 pm 
Hey, thanks a lot man! That is a nice little move! :)

That kind of move is easy to see with basic algebra (e.g. 4x + 2x = 2x (2 + 1)), but harder for me to see using exponents. I will add it to my lookout list when using exponents. ;)
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esledge
 Post subject:
 Post Posted: Tue May 15, 2007 5:31 pm 
Offline
ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
Well done, everyone! A good hint that you should look for something to factor out is the tremendously large numbers involved in this problem. There is no way that you would be expected to actually compute 2^34 or 2^28. Thus, the expression must simplify by some more elegant means: factoring out the common term of 2^28.

_________________
Emily Sledge
Instructor
ManhattanGMAT
Top 
venkatsr
 Post subject: Exponent query
 Post Posted: Sun Dec 28, 2008 1:10 pm 
Hello,

Sorry to update an old thread. I tried this but getting a different answer.

2^34-2^28==>2^28(2^6-1)==> x(34-1)=x(33)==> x(3^1*11)

And I get (E) as the answer. Am I missing something here?


Regards, Sriram
Top 
venkatsr
 Post subject:
 Post Posted: Mon Jan 05, 2009 11:43 am 
Please ignore the above. Realized my mistake.
Top 
RonPurewal
 Post subject:
 Post Posted: Fri Jan 09, 2009 6:54 am 
Offline
ManhattanGMAT Staff


Posts: 7146
venkatsr wrote:
Please ignore the above. Realized my mistake.


here are several other threads that reference this problem.

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
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