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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the greatest prime factor of 8^12 - 2^30? tagged by: Vincen ##### This topic has 2 expert replies and 0 member replies ## What is the greatest prime factor of 8^12 - 2^30? 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. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12442 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 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 â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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