# Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

**Solution:**

Given, the number is 9720.

We have to determine if 9720 is a perfect cube or not.

__Prime factorization__ is a way of expressing a number as a product of its prime __factors__.

A prime number is a number that has exactly two factors, 1 and the number itself.

Using prime factorisation,

So, 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

We observe that 3 and 5 occur without pairs.

Therefore, 9720 is not a perfect cube.

We have to determine the smallest number by which 9720 should be __divided__ to get a perfect cube.

9720 should be divided by 3 × 3 × 5

3 × 3 × 5 = 45

So, 9720/45 = 216

Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3

Therefore, the smallest number to be divided is 45.

**✦ Try This: **Is 930 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

**☛ Also Check:** NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 3 Problem 99**

## Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube

**Summary:**

9720 is not a perfect cube. The smallest number by which 9720 should be divided to get a perfect cube is 45.

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