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Prime Factorization

Written by Rahul Lath

Updated on: 07 Dec 2023

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Calculate Prime Factors of

The Prime Factors of 12 =

2 x

2 x



What is Prime Factorization?

Prime factorization is the mathematical method of multiplying factors of a number together to get the original number. Let’s understand this concept with an example.

What is the prime factorization of 39?

First, we need to check if the given number is a prime number or not. If the number is a prime number then it cannot have more than 2 prime factors. Here, 39 is the given number and it is a composite number so it will have more than 2 factors.

  • Step 1: Divide 39 with the smallest prime number that can divide it. The smallest prime number that is divisible by 39 is 3 so, 39 ÷ 3 = 13.
  • Step 2: Now, let us attempt to divide the quotient 13, with the smallest prime number. But 13 happens to be a prime number and can only be divided by 1 and 13. Dividing 13 and 13 gives us 1: 13 ÷ 13 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 39 are 3 X 13. We can also write it down as 3 and 13, as both of them are prime numbers.

Written by

Rahul Lath

Reviewed by

Arpit Rankwar

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