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What is the greatest prime factor of (4^17)- (2^28)

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Intern
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Joined: 18 Aug 2017
Posts: 30

Kudos [?]: 9 [0], given: 17

GMAT 1: 670 Q49 V33
What is the greatest prime factor of (4^17)- (2^28) [#permalink]

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New post 27 Aug 2017, 07:19
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

90% (00:15) correct 10% (00:01) wrong based on 10 sessions

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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:
\(4^{17}-2^{28}\)
\(= (2^2)^{17}-2^{28}
=2^{28} (2^{6}-1)
=2^{28} (2^3 - 1) (2^3+1)
=2^{28} * 7 * 9\)
So 7 is the greatest prime factor.
This is my own solution, the gmat prep doesnt provide any official solution
[Reveal] Spoiler: OA

Kudos [?]: 9 [0], given: 17

Expert Post
Math Expert
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V
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129457 [0], given: 12201

Re: What is the greatest prime factor of (4^17)- (2^28) [#permalink]

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New post 27 Aug 2017, 07:21
NamVu1990 wrote:
What is the greatest prime factor of \(4^{17}-2^{28}\)

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

[Reveal] Spoiler:
\(4^{17}-2^{28}\)
\(= (2^2)^{17}-2^{28}
=2^{28} (2^{6}-1)
=2^{28} (2^3 - 1) (2^3+1)
=2^{28} * 7 * 9\)
So 7 is the greatest prime factor.
This is my own solution, the gmat prep doesnt provide any official solution


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Kudos [?]: 129457 [0], given: 12201

Re: What is the greatest prime factor of (4^17)- (2^28)   [#permalink] 27 Aug 2017, 07:21
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