What is the greatest prime factor of 8^12 - 2^30? - The Beat The GMAT Forum

What is the greatest prime factor of 8^12 - 2^30?

Expert replies

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Feb 21, 2018 2:02 am

What is the greatest prime factor of $$8^{12}-2^{30}?$$ A. 2
B. 3
C. 5
D. 7
E. 11

The OA is the option D.

Experts, may you show me how can I rewrite the expression and then get the prime factorization? I ask for your help. <i class="em em-disappointed"></i>

Like this post

Source: Beat The GMAT — Problem Solving | Wed Feb 21, 2018 2:02 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 21, 2018 7:50 am

Vincen wrote:What is the greatest prime factor of $$8^{12}-2^{30}?$$ A. 2
B. 3
C. 5
D. 7
E. 11

To determine the greatest prime factor of 8^12 - 2^30, we must find the prime factorization of 8^12 - 2^30

Given: 8^12 - 2^30
Rewrite 8 as 2Â³ to get: (2Â³)^12 - 2^30
Apply Power of Power rule to get: 2^36 - 2^30
Factor out 2^30 to get: 2^30(2^6 - 1)
Evaluate: 2^30(64- 1)
Simplify: 2^30(63)
Factor 63 to get: (2^30)(3)(3)(7)

At this point, we can see that the greatest prime factor is 7

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:09 am

Vincen wrote:What is the greatest prime factor of $$8^{12}-2^{30}?$$ A. 2
B. 3
C. 5
D. 7
E. 11

We can simplify the given expression:

(2^3)^12 - 2^30

2^36 - 2^30

2^30(2^6 - 1) = 2^30(63) = 2^30 x 9 x 7 = 2^30 x 3^2 x 7

So the largest prime factor is 7.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review