Prime Factorization Using the Division Method

Factorization means to write as a product. Therefore, prime factorization is to write as a product of prime numbers.

Integers greater than 1 which are not prime are called composite numbers. All composite numbers can be written as a product of prime numbers. That means that if you pick any composite number, it’s equal to a product of prime numbers. To find the prime numbers (factors), you use a method called prime factorization. There are several ways to do prime factorization. Here, I’ll teach you the division method.

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Rule

The Division Method

1.: See if the number is divisible by $2$ . If it is, put $2$ to the right of the line and your number divided by $2$ to the left of the line. See below for examples that show what it looks like.
2.: If the number isn’t divisible by $2$ , check if it’s divisible by the next prime number, $3$ . If it is, put $3$ to the right of the line, and your number divided by $3$ to the left. If your number isn’t divisible by $3$ , you have to check for the next prime number, which is $5$ . Keep doing this until you find a prime number your number is divisible by.
3.: Each time you find a prime factor, put it on the right side of the line and the previous number divided by the newest prime factor to the left of the line.
4.: Repeat these steps until you get $1$ as the answer to the last division.