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Q.

By which smallest number should 8788 be divided so that the quotient is a perfect cube?


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a

4

b

6

c

8

d

12 

answer is A.

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Detailed Solution

It is given that 8788 must be divided by the smallest number so that the quotient is a perfect cube.
Find the prime factorization of 8878.
2 8788 2 4394 13 2197 13 169 13 13 1 Prime factorization of 8788=2×2× 13×13×13 ¯ .
From the prime factorization, it’s concluded that prime factor 2 doesn’t occur in triplet form but, factor 13 occurs in a triplet. From the information, it’s given that for the product to be a perfect cube; all the prime factors should exist in the triplet.
To make it a perfect cube, the prime factors that aren’t occurring in triplets must be eliminated.
To complete the triplet number, 8788 needs to be divided by 2×2 that is 4.
Hence, the smallest number by which 8788 must be divided so that the quotient becomes a perfect cube is 4.
Thus, option (1) is correct.
 
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