Greatest Prime Factor

[guest]

What is the greatest prime factor of 4^17 - 2^28?

The answer is 7 but I am unable to figure it out --- Is there a shortcut?

Thank you!

[tmmyc]

First, convert 4^17 to (2^2)^17 which equals 2^34.

2^34 - 2^28

Factor out 2^28
2^28 * (2^6 - 1)

Simplify the quantity
2^28 * (64 - 1)
2^28 * 63

Find the prime factors
3, 3, 7, 2 (twenty-eight times)


Hence 7 is the greatest prime factor.

[StaceyKoprince]

Excellent explanation once again tmmyc - thanks! You're making our job easier!