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

[medmond]

Question from GMAC prep practice exam;

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

Choices are: 2,3,5,7,11

The answer is 7, please explain.

I thought it was 2, since 4^17 can be rewritten as 2^(34). Please explain how the answer is 7.

Thankk you.

[StaceyKoprince]

4^17 can be written as 2^34, which gives us:
2^34 - 2^28

I can factor out a 2^28 to get:
2^28(2^6-1)
which is basically a bunch of 2's multiplied by (2^6 - 1)

The first part (the bunch of 2's) has 2 as the only prime factor.

The second part (2^6 - 1) = 64 -1 = 63. 63's prime factorization is 3*3*7. So 7 is the largest prime factor.