Factor out the expression.

\(2^{28}(2^{6}-1)\)

\(2^{28}(64-1)\)

\(2^{28}*63\)

Since all the factors of \(2^{28}\) are 2's, for now, the smallest prime factor is 2.

Next factor out 63 into \(3^{2}*7\).

The prime factors in this expression are 2,3, and 7 now.

7, being the largest, is the greatest prime factor of this expression.