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Question

Find the smallest number by which 9000 should be divided so that the quotient becomes a perfect cube?

A
3
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B
9
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C
27
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D
1
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Solution

The correct option is B 9

Prime factorising 9000, we get,

9000=2×2×2×3×3×5×5×5

=23×32×53

We know, a perfect cube has prime factors in powers of 3.

Here, number of 2's is 3, number of 3's is 2 and number of 5's is 3.

So we need to remove 32 from the factorization to make 9000 a perfect cube.

Hence, the smallest number by which 9000 must be divided to obtain a perfect cube is 32=9.

Therefore, option B is correct.

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