What is the greatest prime factor of

[Lookingfor700GMAT]

4^-2^28

2
3
5
7
11

Please can you explain how this is solved.

[Lookingfor700GMAT]

To be clear the stimulus is

4^17-2^28

[Osirus@VeritasPrep]

rewrite 4^17 as (2^2)^17

This equals 2^34

Now you have to factor 2^34 - 2^28

this equals 2^28 (2^6 - 1)

this equals 2^28 (64-1)

This equals 2^28 (63)

63 broken into prime factors is 3^2 * 7

Therefore, the greatest prime factor is 7

[Lookingfor700GMAT]

Awesome stuff. Thanks!

[Lookingfor700GMAT]

Actually can you explain these steps again please

rewrite 4^17 as (2^2)^17

This equals 2^34

Now you have to factor 2^34 - 2^28

this equals 2^28 (2^6 - 1)