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# Number properties question - prime factors

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Number properties question - prime factors [#permalink]  01 May 2011, 01:51
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What is the greatest prime factor of 4^17 - 2^28?

A) 2
B) 3
C) 5
D) 7
E) 11
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Re: Number properties question - prime factors [#permalink]  01 May 2011, 02:11
chloeholding wrote:
What is the greatest prime factor of 4^17 - 2^28?

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

Sol:
4^{17}-2^{28}=(2^{2})^{17}-2^{28}=2^{34}-2^{28}=2^{28}*2^{6}-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7

The prime factors of the number are 2,3,7 of which 7 is the greatest.

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Re: Number properties question - prime factors [#permalink]  02 May 2011, 20:36
= 2^34 - 2^28

= 2^28 (2^6 - 1)

= 2^28 * 63

= 2^28 * 7*9

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Re: Number properties question - prime factors [#permalink]  02 May 2011, 20:42
2^28 * 63

63 = 3^2 * 7

Hence 7
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Re: Number properties question - prime factors   [#permalink] 02 May 2011, 20:42
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# Number properties question - prime factors

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