To Find if the Given Number is a Perfect Cube

How to find if the given number is a perfect cube?

If the prime factors of a number are grouped in triples of equal factors, then that number is called a perfect cube.

Examples to find if the given number is a perfect cube:

1. Find out if the following are perfect cubes.

(i) 250

(ii) 5832

(i) 250

Solution:

Resolving 250 as the product of prime factors

$Perfect Cube$

250 = 2 × 5 × 5 × 5

Since 2 does not exist in product of triples.

Therefore, 250 is not a perfect cube.

(ii) 5832

Solution:

Resolving 5832 as the product of prime factors

$Perfect Cube$

5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Since, they are grouped in triples.

Therefore, 5832 is a perfect cube.

2. Find the smallest number by which 1944 must be multiplied so that the product is a perfect cube.

Solution:

Resolving 1944 as the product of prime factors

$Perfect Cube$

1944 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3

In order to make 1944 a perfect cube, it must be multiplied by 3.

3. Find the smallest number by which 4394 must be divided so that the quotient is a perfect cube.

Solution:

Resolving 4394 as the product of primes

$Perfect Cube$