Encyclopedia>Numbers and Quantities>Numbers>Prime Numbers and Factorization>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

- 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.

Example 1

**Factor the number 24 into primes **

24 is the product of all the prime numbers in the circles. That means you get

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

Example 2

**Factor the number 100 into primes **

100 is the product of all the prime numbers in the circles. That means you get

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

Example 3

**Factor the number 144 into primes **

144 is the product of all the prime numbers in the circles. Then you have

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

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Prime Factorization Using the Division Method

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