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Greatest Prime Factor Question

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Re: Greatest Prime Factor Question

by parallel_chase » Fri Nov 28, 2008 2:00 pm
GMATJeff wrote:Can anyone help explain an easy solution to this problem?

1. What is the greatest Prime Factor of 4^17 - 2^28?

The answer is 7, but I'm not clear on how it is derived.

Thanks!
4^17 - 2^28

4^17 = 2^17 * 2^17 = 2^34

2^34 - 2^28 = 2^28 (2^6 -1)

2^6 = 64

2^28 (64-1) = 2^28 * 63 = 2^28 * 7 * 3 * 3

greatest prime factor = 7

Hope this helps.
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