Please help with this one

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tonker
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Topic: Please help with this one
PostTue Jan 16, 2007 5:33 pm
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What is the greatest prime factor of 4^17 - 2^26?

a) 2
b) 3
c) 5
d) 7
e) 11

Source: GMAT Prep test

Thanks,
Vito
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rajs.kumar
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PostTue Jan 16, 2007 6:09 pm
Probably you should try using this

2 ^ 2 ^ 17 - 2 ^ 26 = 2 ^ 26 (2 ^ 8 - 1) = 2 ^ 26 x 255
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tonker
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PostTue Jan 16, 2007 6:39 pm
rajs.kumar wrote:
Probably you should try using this

2 ^ 2 ^ 17 - 2 ^ 26 = 2 ^ 26 (2 ^ 8 - 1) = 2 ^ 26 x 255
I don't see how that would solve the problem above. Please advise.
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sumitkrishna
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PostTue Jan 16, 2007 10:37 pm
4^17 - 2 ^ 26

(or) 2^34 - 2 ^26

(or) 2^26(2^8-1)

(or) 2*2^25*255

Factors of 255 are 1,3,5,15,17,51,85,255

Hence the prime factors of the whole expression are 2,3,5,17.

Highest is 5 (among the answer choices provided)

Therefore, should be C (as per my understanding of this problem).
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