Prime Factorization

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.

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.