Question

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided so that quotient is a perfect cube.

Answer 1

Step-by-step explanation:

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Answer 2

Therefore the required smallest number is '45'.

Given:

The number = 9720

To Find:

Whether 9720 is a perfect cube or not. if not the smallest number should be found by which if the number is divided then the quotient becomes a perfect cube.

Solution:

The given question can be answered very easily as shown below.

Prime Factorization of 9720:

2 I  9720  

2 I  4860  

2 I  2430  

3 I  1215  

3 I  405  

3 I  135  

3 I   45  

3 I    15  

        5  

⇒ The prime factors of 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

As only '2' was repeated 3 times and '3' was repeated 5 times and 5 got only once so 9720 is not a perfect cube.

Hence if '9720' is divided by '3 × 3 × 5' the quotient we get will be '2 × 2 × 2 × 3 × 3 × 3' which is a perfect cube.

So the smallest number should be 3 × 3 × 5 = 45

Therefore the required smallest number is '45'.

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