How to verify if a number is perfect cube

Learn how to verify if a number is perfect cube using Prime Factorization Method. It is the method to use to find out if a given number is a perfect cube or not if you want accurate results. Before going into the details of the Prime Factorization Method, it is helpful to know what Prime factors are.

Prime numbers are those numbers which are divisible only by 1 and the number itself. These numbers do not have any other divisible factors.

Prime numbers such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……. are also known as the prime factors.
Now, we shall see how Prime Factorization Method is done from the below steps.
Step 1: Find the prime factors of the given number.
Step 2:Group the factors in 3’s of equal factors.
Step 3:After grouping,
If you are not left with any separate single or double factor, then the given number is a perfect cube.
If you are left with any separate single or double factor, then the given number is not a perfect cube.
Let us consider some examples to understand the Prime Factorization Method better.

Example of a number which is a perfect cube.

Example1:Verify if 216 is a perfect cube.
Step1:We start by finding prime factors of 216.
Prime factors of 216 are 2x2x2x3x3x3
Step 2: Grouping the factors into 3’s
(2x2x2) x (3x3x3)
Step 3: After grouping, we notice that no factor is left.
Therefore we can say that 216 is definitely a perfect cube.

Example of a number which is not a perfect cube.

Example 2:Verify if 1024 is a perfect cube
Step1:We start by finding prime factors of 1024.
Prime factors of 1024 are 2x2x2x2x2x2x2x2x2x2
Step 2:Grouping the factors into 3’s
(2x2x2) x (2x2x2) x (2x2x2) x 2
Step 3: After grouping, we notice that factor 2 is left.
Therefore we can say that 1024 is not a perfect cube.