What is the greatest prime factor of 4^17 - 2^26?	Choices:
A) 2  B) 3  C) 5  D) 127  E) 11
I'm happy to help with this.   We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*17) = 2^34   That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)   So, 4^17 - 2^26 = 2^34 - 2^26 = 2^(26 + 8) - 2^26 = (2^26)*(2*8) - 2^26 = (2^8 - 1) *(2^26)   = (128 - 1)*(2^26) = 127*(2^26)   The prime factors of 63 are 127, so the largest prime factor is 127, answer choice D.   Here's a blog you may find helpful.   http://magoosh.com/gmat/2012/gmat-math-factors/   Does all that make sense? Please let me know if you have any further questions.   Mike   Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.   127
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What is the greatest prime factor of 4^17 - 2^26?