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Prime Factorization Using a Factor Tree

Integers greater than 1 which are not prime are called composite numbers. All composite numbers can be written as a product of prime numbers. To find these prime numbers (factors), you do something called prime factorization. There are several methods for that. Here I’ll show you how to use a factor tree.

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Rule

Factor Trees

1.: Find a product that has the number you want to factorize as the answer
(example: $8 \cdot 3 = 24$ ).
2.: Check if any of the factors are prime numbers. If you have a prime number, put a ring around it (3 is a prime number, put a ring around it).
3.: If one or both of the numbers are not prime numbers, you need to find a product that is equal to the number(s) that are not prime numbers. (8 is not a prime number, you find the product $4 \cdot 2$ ).
4.: Check if any of these factors are prime numbers. If you have a prime number, put a ring around it (2 is a prime number, put a ring around it).
5.: If one or both of the numbers are not prime numbers, you have to find a new product that equals the number(s) that are not prime numbers. (4 is not a prime number, you find the product $2 \cdot 2$ ).
6.: Check if any of the factors are prime numbers. If you have a prime number, put a ring around it. (2 is a prime number, put a ring around it).
7.: Repeat the steps until all the arrows end in a number with a ring around it.
8.: The numbers with rings around them are the prime factors of your number.