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# What is the highest prime number that is a factor of 4^17 -

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Manager
Joined: 18 Jan 2007
Posts: 97
Followers: 1

Kudos [?]: 5 [0], given: 0

What is the highest prime number that is a factor of 4^17 - [#permalink]  24 Aug 2007, 17:36
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Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
What is the highest prime number that is a factor of 4^17 - 2^28?
a) 2
b) 3
c) 5
d) 7
e) 11

Folks this problem I have spent one hour on trying to find a way to solve under 2 minutes. I am absolutely boggled by how to do it. Please tell me this is a difficult problem, maybe even a very difficult one.

Help, thanks.
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 180 [1] , given: 2

1
KUDOS
yes Dr..this is a very difficult problem

however in GMAT world this is 500 level question

here is how to do it in 20 secs...

4^17=2^34

2^34 - 2^28 => 2^28(2^6 -1) OK?

2^6=64.. 64-1 =63 guess what are the prime factors of 63..7*3^2

highest prime is 7
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

fresinha12 wrote:
yes Dr..this is a very difficult problem

however in GMAT world this is 500 level question

here is how to do it in 20 secs...

4^17=2^34

2^34 - 2^28 => 2^28(2^6 -1) OK?

2^6=64.. 64-1 =63 guess what are the prime factors of 63..7*3^2

highest prime is 7

Perfect !!!

I second (D)

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