Greatest Prime Factor

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Greatest Prime Factor

by relaxin99 » Sun Feb 15, 2009 1:26 pm
What is the greatest prime factor of 4^17-2^28

A) 2
B) 3
C) 5
D) 7
E) 11

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by DanaJ » Sun Feb 15, 2009 1:35 pm
4^17 = (2^2)^17 = 2^34.
This means that 2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 * 63 = 2^28 * 3^2 * 7.
Greatest prime factor is 7.

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by Bidisha800 » Sun Feb 15, 2009 2:11 pm
2^34-2^28
=2^28*(2^6-1)
=2^28*63
=2^28*3^3*7

Answer =7

(D)
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