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What is the greatest prime factor of 2^100 2^96 ? A.

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What is the greatest prime factor of 2^100 2^96 ? A. [#permalink]  09 Oct 2005, 00:51
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What is the greatest prime factor of 2^100 â€“ 2^96 ?

A. 2

B. 3

C. 5

D. 7

E. 11

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Cheers, Rahul.

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Joined: 01 Oct 2005
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C. 5 [#permalink]  09 Oct 2005, 02:38
2^100 - 2^96 = (2^4)*(2^96) - (2^0)*(2^96)
= (16-1)*(2^96)
= 15 * 2^96
= 3*5*2^96

The prime factors are 2,3,5 and the greatest prime is 5.
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2^100 - 2^96 = 2^96(2^4 - 1) = 2^96(5*3)

So the greatest prime factor is 5
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