Greatest prime factor of $4^{17}-2^{28}$?

Question

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!

Answer 1

2⁶ - 1 = 64 - 1 = 63

63 = 9(7) = 3²(7)

4¹⁷ - 2²⁸ = 2²⁸(3²)(7)