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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: 94

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

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24 Aug 2007, 18:36
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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.

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Current Student
Joined: 28 Dec 2004
Posts: 3345

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Location: New York City
Schools: Wharton'11 HBS'12

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24 Aug 2007, 19:40
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

Kudos [?]: 322 [1], given: 2

VP
Joined: 08 Jun 2005
Posts: 1143

Kudos [?]: 254 [0], given: 0

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24 Aug 2007, 23:15
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)

Kudos [?]: 254 [0], given: 0

24 Aug 2007, 23:15
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