Greatest prime factor of $4^{17}-2^{28}$ I have seen the solution to this problem. 

What is the greatest prime factor of $ \ 4^{17} - 2^{28} \ $?

Answer: 7
$$ 4^{17}-2^{28} \ = \ 2^{34}-2^{28} \ = \ 2^{28} \ (2^6-1) \ = \ 2^{28} \ \cdot \ 63 \ = \ 2^{28}\ \cdot \ 3^2 \ \cdot \ 7 $$
I understand the problem up to this part: $2^{28} \ (2^6-1) \ $ .
Why did this occur? I can't explain it.
Thanks!

You are asking how you went from $2^{34} - 2^{28} = 2^{28}(2^6-1)$? You are factoring out $2^{28}$ from both of the numbers. $2^{34} - 2^{28}=(2^{34} - 2^{28})*\frac{2^{28}}{2^{28}}=\frac{2^{34} - 2^{28}}{2^{28}}*2^{28}=(2^6-1)*2^{28}$
