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What is the greatest prime factor

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prengasn
 Post subject: What is the greatest prime factor
 Post Posted: Thu Aug 13, 2009 11:04 am 
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Course Students


Posts: 9
What is the greatest prime factor of 4^17 - 2^28

a.2
b.3
c.5
d.7
e.11

I apreciate an expanation.
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Kweku.Amoako
 Post subject: Re: What is the greatest prime factor
 Post Posted: Thu Aug 13, 2009 1:34 pm 
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Posts: 47
4^17 - 2^28.....the trick here is to simplify and break the expression down into prime factors

4^17 = (2^2) ^17 = 2^34

so the problem becomes 2^34 - 2^28

at this point we can factorize out 2^28

there 2^34 - 2^28 = 2^28( (2^6) - 1)

we know 2^6 = 64 there 2^6 -1 = 63

so 2^34 - 2^28 = 2^28 ( 63 ) = 2^28 ( 7 * 9 ) = 2^28(7* 3^2)

so the prime factors are 2, 3 and 7 and there it's obvious the answer is 7
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prengasn
 Post subject: Re: What is the greatest prime factor
 Post Posted: Thu Aug 13, 2009 8:43 pm 
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Course Students


Posts: 9
Thanks a lot. Great explanation.
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RonPurewal
 Post subject: Re: What is the greatest prime factor
 Post Posted: Fri Aug 21, 2009 7:39 pm 
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ManhattanGMAT Staff


Posts: 7146
please search for problems before you post them in the forum. this particular problem has been posted almost ten different times in the last couple of years.

here are two:

what-is-the-greatest-prime-factor-of-4-17-2-28-t411.html

what-is-the-greatest-prime-factor-of-4-17-2-28-t346.html

the latter of these two contains links to about 5 more versions, too.
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