Greatest prime factor

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Viper83: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon Aug 16, 2010 4:42 am

by Viper83 » Tue Nov 23, 2010 7:00 am

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

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

d

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Source: Beat The GMAT — Problem Solving | Tue Nov 23, 2010 7:00 am

abhishekg21: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Tue May 11, 2010 5:46 am; Thanked: 3 times

by abhishekg21 » Tue Nov 23, 2010 7:20 am

(4 ^17)-(2^28)=(2^34)-(2^28)=2^28(2^6-1)=2^28*63=2^28*7*9

since largest prime number in 2^28*7*9 is 7 so answer is d

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Brian@VeritasPrep: GMAT Instructor; Posts: 1031; Joined: Thu Jul 03, 2008 1:23 pmFollowed by: 255 members; Location: Malibu, CA; Thanked: 716 times; GMAT Score:750

by Brian@VeritasPrep » Tue Nov 23, 2010 10:58 am

Good question - and like many exponent questions this one comes down to:

1) Finding common bases

2) Factoring common terms to turn addition/subtraction into multiplication

First, we need to get a common base of 2:

2^34 - 2^28

Then we can factor out the 2^28 term:

2^28 (2^6 - 1)

Now we know that the greatest prime factor of 2^28 is 2 (2 is its only PRIME factor), so we're left with 2^6 - 1, which is:

64-1 = 63

63 = 9*7 = 3*3*7

7 is the greatest prime factor, so the answer is D.

Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.

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