gmat prep 2 prime number

[gmat]

does anyone know how to get to the right answer 7?

[RonPurewal]

please follow the forum guidelines, as quoted in the 'sticky' at the top of the thread:

4) Only use image files for complicated diagrams or other things that cannot easily be typed in (eg, geometric shapes or seriously complex fractions). It takes significantly longer for us to download and view image files - the more we have to do that, the fewer problems we can get through.

please transcribe this problem into the forum, and then we'll answer it.

thanks.

[Guest]

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

2
3
5
7
11

OA is 7.

I figured out the right answer and what I was doing wrong.

In order to solve this:

get everything in the same base

(2^2)^17 - 2^28
2^34 - 2^28
2^28 (2^6 -1)
2^28 (64-1)
2^28 * 63

the factors of 63 is 9 *7

7 is the biggest prime

(originally, I just subtract 28 from 34, but that is WRONG)

[RonPurewal]

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

2
3
5
7
11

OA is 7.

I figured out the right answer and what I was doing wrong.

In order to solve this:

get everything in the same base

(2^2)^17 - 2^28
2^34 - 2^28
2^28 (2^6 -1)
2^28 (64-1)
2^28 * 63

the factors of 63 is 9 *7

7 is the biggest prime

(originally, I just subtract 28 from 34, but that is WRONG)

well played.

[StaceyKoprince]

Hi, guys - please follow the posting guidelines. Your subject line should be the first 5 to 8 words of the problem. Thanks!