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

[GMAT 5/18]

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!

[vanD]

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

[GMAT 5/18]

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!

[Guest]

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

[GMAT 5/18]

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.

[esledge]

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.

[venkatsr]

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

[venkatsr]

Please ignore the above. Realized my mistake.

[RonPurewal]

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