## Que: If both 11 and $$7^2$$ are factors of $$a\cdot4^5\cdot6^3\cdot7$$, then what is the.....

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### Que: If both 11 and $$7^2$$ are factors of $$a\cdot4^5\cdot6^3\cdot7$$, then what is the.....

by [email protected] Revolution » Mon Aug 09, 2021 8:42 pm

00:00

A

B

C

D

E

## Global Stats

Que: If both 11 and $$7^2$$ are factors of $$a\cdot4^5\cdot6^3\cdot7$$, then what is the smallest possible value of a?

(A) 7
(B) 11
(C) 49
(D) 77
(E) 539 Math Revolution

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[Course] Starting $79 for on-demand and$60 for tutoring per hour and $390 only for Live Online. Email to : [email protected] Elite Legendary Member Posts: 3991 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Re: Que: If both 11 and $$7^2$$ are factors of $$a\cdot4^5\cdot6^3\cdot7$$, then what is the..... by [email protected] Revolution » Tue Aug 10, 2021 9:20 pm Solution: Express the given number $$a\cdot4^5\cdot6^3\cdot7$$ in prime factors as $$a\cdot2^{10}\cdot2^3\cdot3^3\cdot7$$ For 11 to be the factor it should be contained in it. If we remove ‘a’ then we don’t have 11. Hence a = 11. => 7 is contained already and hence we need 1 more 7 so that $$7^2$$ is the factor and hence 7 should also be in a. Thus, smallest value of a = 7 * 11 = 77 Therefore, D is the correct answer. Answer D Math Revolution The World's Most "Complete" GMAT Math Course! Score an excellent Q49-51 just like 70% of our students. [Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions. [Course] Starting$79 for on-demand and $60 for tutoring per hour and$390 only for Live Online.
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