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On the GMATPrep software: What is the largest prime number

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On the GMATPrep software: What is the largest prime number [#permalink] New post 26 Jul 2006, 19:23
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On the GMATPrep software:
What is the largest prime number for 4^17-2^28.
The answer is 7, but how do you get that.

I know 4^17=2^34 but where to I go from there?
4^17-2^28=2^34-2^28

Thank you for any answers...
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Re: PS: Subtracting exponents...shortcuts? [#permalink] New post 26 Jul 2006, 19:28
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lacey.griffith wrote:
On the GMATPrep software:
What is the largest prime number for 4^17-2^28.
The answer is 7, but how do you get that.

I know 4^17=2^34 but where to I go from there?
4^17-2^28=2^34-2^28

Thank you for any answers...


As you have mentioned you know that 4^17-2^28=2^34-2^28

Factor out a 2^28 * (2^6 - 1) = 2^28 * 63

You know that 63 = 9*7
Therefore 7 is your answer...
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Re: PS: Subtracting exponents...shortcuts? [#permalink] New post 26 Jul 2006, 21:36
lacey.griffith wrote:
On the GMATPrep software:
What is the largest prime number for 4^17-2^28.
The answer is 7, but how do you get that.

I know 4^17=2^34 but where to I go from there?
4^17-2^28=2^34-2^28

Thank you for any answers...

4^17-2^28=2^34-2^28
= 2^28 (2^6 -1)
= 2^28 * 63.
So largest prime factor is 7.
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 [#permalink] New post 27 Jul 2006, 01:42
2^17 - 2^28
=> 2^34 - 2^28
=> 2^28( 2^6 -1)
=> 2^28 (64-1)
=>2^28 * 63
=>2^28 * 3^2 * 7

hence 7 is the largest prime number
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Thank you everyone. [#permalink] New post 27 Jul 2006, 02:30
It's amazing how obvious it becomes when someone else does the work for you. :)
Thank you everyone.   [#permalink] 27 Jul 2006, 02:30
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On the GMATPrep software: What is the largest prime number

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