Problem Solving

What is the largest prime factor of 4^17 – 2^28?

1. 7

I think this one has been answered before, but I'll help out anyway:

The first thing I'd do is turn the 2^28 into 4^14, giving you 4^17 - 4^14.

Then, I'd factor our the 4^14 leaving me with

4^14(4^3 - 1)

I know the prime factors represented by 4^14 will just be 28 2's. So as long as I get something more than a 2 as a prime factor of 4^3 -1 then that will be the answer. 4^3 - 1 = 63 whose prime factors are 3, 3, 7. So the prime factorization of this difference is 28 2's, 3, 3, and 7, the largest, of course, is 7.

Nice response. I like that.

Understandable response! Good job!