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

Author Message
Intern
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33
What is the greatest prime factor of (4^17)- (2^28)  [#permalink]

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27 Aug 2017, 07:19
00:00

Difficulty:

35% (medium)

Question Stats:

91% (00:18) correct 9% (00:01) wrong based on 11 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

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

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Math Expert
Joined: 02 Sep 2009
Posts: 55150
Re: What is the greatest prime factor of (4^17)- (2^28)  [#permalink]

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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

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

Discussed here: what-is-the-greatest-prime-factor-of-104757.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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