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4^17 - 2^28: Find the greatest prime factor

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4^17 - 2^28: Find the greatest prime factor

by Lasve » Tue Dec 20, 2011 2:17 pm
4^17 - 2^28
Find the greatest prime number
a)2
b)3
c)5
d)7
e)11


Hi, I've my Gmat test in 2 days, and still I do not have any idea about this one, can anybody help me??
I'm sure there is something stupid I'missing..
Thank's a lot!!!
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by neelgandham » Tue Dec 20, 2011 3:16 pm
Lasve wrote: Find the greatest prime number factor of 4^17 - 2^28
a)2
b)3
c)5
d)7
e)11
Hi, I've my Gmat test in 2 days, and still I do not have any idea about this one, can anybody help me??
I'm sure there is something stupid I'missing..
Thank's a lot!!!
I'm sure that you have missed a part of the question. The solution provided below is for the NEW question(corrected in red above).

4^17 - 2^28
= 4^17 - 2^(2*14)
= 4^17 - 4^14
= 4^14*(4^3 - 1)
= 4^14*(64 - 1)
= (2^28)*(63)
= (2^28)*(3^2)*(7)

2,3,7 are the prime number factors of 4^17 - 2^28 of which 7 is the largest number. Ans D
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by Lasve » Tue Dec 20, 2011 3:24 pm
OMG!!!
I feel such an Idiot, both for the answer and the question.

Of course the question you restated is the right one!

and about the answer there was something really simple I was missing,

Thank you!!
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by neelgandham » Tue Dec 20, 2011 3:32 pm
No Problemos! Things don't go our way at times !

Out of context: I know a guy who scored a 750 (with a 51 in Quant) and who in one of the GMAT prep tests took 10 minutes to solve this problem -> https://www.beatthegmat.com/og-ps-171-ea ... 99852.html . It happens with every one, Glazed eyes you see, so you need not worry one bit ;)
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