Checking if perfect square by prime factorisation

Last updated at August 14, 2026 by

Here,

  • We do prime factorization of the number
  • If the prime factorization forms pairs, then it is a perfect square
  • If it doesn’t, then it isn't a perfect square

Let’s take some examples

 

Is 32 a perfect square?

13.jpg

Here, we do not get perfect square as one 2 is left alone.

So, 32 is not a perfect square

 

Is 120 a perfect square?

Checking if perfect square by prime factorisation - Part 2

Here, 2, 3, 5 are not in pairs

So, 120 is not a perfect square

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