Flexxice wrote:

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

A) 2

B) 3

C) 5

D) 7

E) 11

First of all 4^17 = (2^2)^17 = 2^34

So, 4^17 - 2^28 = 2^34 - 2^28

= 2^28(2^6 - 1) [factored out 2^28]

= 2^28(2^3 + 1)(2^3 - 1) [factored again]

= 2^28(8 + 1)(8 - 1) [evaluated]

= 2^28(9)(7) [evaluated]

= 2^28(3)(3)(7)

So, as you can see, the greatest prime factor is 7

Answer = D

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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