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greatest prime factor

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Joined: 08 Apr 2009
Posts: 1200

Kudos [?]: 477 [0], given: 19

Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
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greatest prime factor [#permalink]

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New post 17 Jul 2009, 14:39
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A
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D
E

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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

[Reveal] Spoiler: Official Answer
D

Last edited by asimov on 19 Jul 2009, 21:27, edited 2 times in total.

Kudos [?]: 477 [0], given: 19

Manager
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Joined: 08 Jul 2009
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Kudos [?]: 89 [0], given: 13

Re: greatest prime factor [#permalink]

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New post 17 Jul 2009, 18:54
Are you sure there is not a typo in this q?

Kudos [?]: 89 [0], given: 13

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Joined: 15 Apr 2008
Posts: 50

Kudos [?]: 23 [0], given: 8

Location: Moscow
Re: greatest prime factor [#permalink]

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New post 18 Jul 2009, 01:18
sher676 wrote:
Are you sure there is not a typo in this q?

Yes, the equation should be 4^(17)-2^(28)?

Kudos [?]: 23 [0], given: 8

VP
VP
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B
Joined: 08 Apr 2009
Posts: 1200

Kudos [?]: 477 [0], given: 19

Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Premium Member
Re: greatest prime factor [#permalink]

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New post 18 Jul 2009, 07:44
Sorry, I mistyped it. I just edited the original post.

Kudos [?]: 477 [0], given: 19

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Re: greatest prime factor [#permalink]

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New post 19 Jul 2009, 19:38
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4^17 - 2^28
= 2^34 - 2^28
= 2^28 ( 2^6 - 1)
= 2^28 (64 - 1)
= 2^28 (63)

As you can see the greatest prime factor of 63 is 7.

Hence 2^28 * 63 also has 7 as the greatest prime factor. Therefore answer should be D. What is the OA?

Kudos [?]: 133 [2], given: 0

VP
VP
avatar
B
Joined: 08 Apr 2009
Posts: 1200

Kudos [?]: 477 [0], given: 19

Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Premium Member
Re: greatest prime factor [#permalink]

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New post 19 Jul 2009, 21:27
thanks for the great explanation. the OA is D.

Kudos [?]: 477 [0], given: 19

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Kudos [?]: 34 [0], given: 11

Re: greatest prime factor [#permalink]

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New post 20 Jul 2009, 03:41
Grt Explanation sdrandom1 +1

Kudos [?]: 34 [0], given: 11

Re: greatest prime factor   [#permalink] 20 Jul 2009, 03:41
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