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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 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 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 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

Factor tree of 24

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

24 = 2 2 2 3.

Example 2

Factor the number 100 into primes

Factor tree of 100

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

100 = 2 2 5 5.

Example 3

Factor the number 144 into primes

Factor tree of 144

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

144 = 2 2 2 2 3 3.

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