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power problem..

by ska7945 » Wed Aug 13, 2008 1:18 am
What is the greatest prime factor of 2^100-2^96?

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

answer C

Also can you explain...
2^4-2^2=3(2^2)
2^5-2^3=3(2^4)
i dont understand this concept. please help me out. thx.
let's beat GMAT.
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by santa_dem » Wed Aug 13, 2008 1:24 am
2^100-2^96=2^96*(2^4-1)=2^96*(16-1)=15*2^96=2^96*3*5.

The prime factor of (2^100-2^96) are 2,3 and 5.

The greatest is 5.

Answer - C.

Same thing with 2^4-2^2=2^2*(2^2-1)=2^2*(4-1)=3*2^2
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by s_kaks » Wed Aug 13, 2008 3:05 am
2^100-2^96=2^96*(2^4-1)
=2^96*(16-1)
=2^96*(15)
=2^96*(3*5)

Therefor Greatest prime factor is 5.

ans. C
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