prime factor

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scmetzger: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Sep 12, 2008 4:47 pm

by scmetzger » Mon May 25, 2009 11:44 am

Please help me and explain this answer to me.

What is the greatest prime factor of 4^17 - 2^28?

The answer is: 7.

Thanks for your help.

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Source: Beat The GMAT — Problem Solving | Mon May 25, 2009 11:44 am

tdadic84: Master | Next Rank: 500 Posts; Posts: 111; Joined: Sat Sep 27, 2008 12:41 pm; Thanked: 1 times

by tdadic84 » Mon May 25, 2009 11:51 am

im no pro like some ppl on here...but gmat is in 10 days..so let me give it a shot..

break down 4^17 - 2^28

to (2^17)2^17) - 2^28
= 2^34 - 2^28
= 2^28(2^6 - 1)
= 2^28 (63)

Break down 63 into the prime factorization and you get 7 as the highest prime...7 X 3^2..

hence 7...

hope i am correct...

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