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Greatest prime factor

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by Anurag@Gurome » Sun Oct 09, 2011 8:26 am
Cheese12 wrote:What is the greatest prime factor of 4^17 - 2^28?
4^17 - 2^28 = (2^2)^17 - 2^28 = 2^34 - 2^28 = (2^28)*(2^6 - 1) = (2^28)*(64 - 1) = (2^28)*63 = (2^28)*(3^2)*7

Hence, greatest prime factor of the given expression is 7.

The correct answer is D.
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by parul9 » Sun Oct 09, 2011 8:31 am
It's D!
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by MBA.Aspirant » Sun Oct 09, 2011 8:35 am
4^17 - 2^28

2^34 - 2^28

2^28 ( 64 - 1)

2^28 * 63

= 2^28 * 3^2 * 7

so greatest prime factor = 7
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by Abhishek009 » Sun Oct 09, 2011 8:52 am
Cheese12 wrote:What is the greatest prime factor of 4^17 - 2^28 ?
A) 2
B) 3
C) 5
D) 7
E) 11

4^17 can be written as 2^34


So , 4^17 - 2^28 can be written down as -


2^34 - 2^28


Or, 2^28 ( 2^6 - 1 )


or , 2^28 ( 64 - 1 ) => 2^28 ( 63 )


Now , 2^28 ( 63 ) = 2^28 ( 7 * 3^2 )

2^28 ( 7 * 3^2 )

Of the above mentioned factors 7 is the highest Prime factor ( Amongst 2 , 3 and & 7 ) so , the greatest prime factor is 7....
Abhishek
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