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Q.

What is the smallest number by which 3087 must be divided, so that the quotient is a perfect cube?


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a

8

b

9

c

10

d

12 

answer is B.

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Detailed Solution

It is required to find the smallest number by which 3087 must be divided, so that the quotient is a perfect cube.
Now, using prime factorization and grouping the factors in triple form, represent the provided number as a product of prime factors.
⇒3087=3×3×7×7×7= 3 2 × 7 3  
We observe that just two 3s appear in the prime factorization of 3087. So, 3087 must be divided by 9 so that the quotient is a perfect cube.
So, the fewest number by which 3087 must be divided to produce a quotient that is an exact cube is 9.
Therefore, option 2 is correct.
 
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