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

- 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.

But how do you know which numbers are divisible by the different prime numbers? For the answer to that, check out the entry about divisibility.

Example 1

**You need to find the prime factors of the number 24.**

$24$ is the product of the prime numbers in the column to the right. That makes

$$24={2}\cdot {2}\cdot {2}\cdot {3}.$$ |

Example 2

**You need to find the prime factors of the number 100.**

$100$ is the product of the prime numbers in the column to the right. That makes

$$100={2}\cdot {2}\cdot {5}\cdot {5}.$$ |

Example 3

**You need to find the prime factors of the number 144.**

$144$ is the product of the prime numbers in the column to the right. That makes

$$144={2}\cdot {2}\cdot {2}\cdot {2}\cdot {3}\cdot {3}.$$ |