## 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

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### 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.