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Cubes and Cube Roots

  • A number is said to be a perfect cube if each of its prime factors appears in group of three.
  • Prime factorization method can be used to check whether a number is a perfect cube or not.

For example, 5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Here, each of the prime factors occurs in groups of three. Hence, 5832 is a perfect cube.


  • We can use the method of prime factorization to find the smallest number with which the given number must be multiplied with or divided by to obtain a perfect cube.


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