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If 9720 is a perfect cube, then the smallest number by which it should be divided to get a perfect cube is:

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answer is D.

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Detailed Solution

The given number is

9720

.
The prime factors of

9720

are,

9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

Here

2

is grouping in one triplet,

3

is grouping in one triplet.
But a pair of

3

and single

5

does not occur in triplets.
So,

9720

is not a perfect cube.
To make

9720

a perfect cube, there should be triplets of prime factors.
There is one triplet of

2

and one triplet of

3

.
Another pair of

3

and

5

is single.
So, the least number by which

9720

be divided to make it a perfect cube is,

3 × 3 × 5 = 45

9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

972045 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5 3 × 3 × 5

216 = 2 × 2 × 2 × 3 × 3 × 3

which is a cube number.
The least number that divides 9720 to get the cube number is

45

.
Hence, option 4 is correct.

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