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# Prime Factorization

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In this section, we learn how to find the prime factorization of a number. We start out by learning about the difference between prime and composite numbers. A prime number is a whole number that is larger than 1, and only divisible by itself or 1. We will find that 2 is the only even prime number. Every even number larger than 2 will be divisible by 2 and therefore not fit the definition of a prime number. A composite number is a whole number that is greater than 1 and divisible by some number other than itself and 1. The numbers 0 and 1 do not fall into either category. They are not considered to be prime numbers or composite numbers.

Example 1: Determine if 5, 20, and 32 are prime, composite, or neither

5 - prime, it is only divisible by itself 5 or 1

20 - composite, the number is even and larger than 2

32 - composite, the number is even and larger than 2

Next, we will think about how to break a number down into the product of its prime factors. Breaking a number down into the product of prime factors is known as finding its prime factorization. This process is very simple and in most cases, one can use a visual aid such as a factor tree or division ladder.

Prime Factorization of a Number:

Start with any 2 factors of the number: 120 = 60 x 2

Check to see if either factor is prime: 60 is not prime, 2 is prime

Circle 2 and continue working on 60

120 = 60 x 2

Repeat the process on 60, find any 2 factors: 60 = 30 x 2

Check to see if either factor is prime: 30 is not prime, 2 is prime

Circle 2 and continue working on 30

120 = 30 x 2 x 2

Repeat the process on 30, find any 2 factors: 30 = 15 x 2

Check to see if either factor is prime: 15 is not prime, 2 is prime

Circle 2 and continue working on 15

120 = 15 x 2 x 2 x 2

Repeat the process on 15, find any 2 factors: 15 = 5 x 3

Check to see if either factor is prime: 5 is prime, 3 is prime

Circle 5 and 3, we have found our prime factorization:

120 = 5 x 3 x 2 x 2 x 2

Example 1: Determine if 5, 20, and 32 are prime, composite, or neither

5 - prime, it is only divisible by itself 5 or 1

20 - composite, the number is even and larger than 2

32 - composite, the number is even and larger than 2

Next, we will think about how to break a number down into the product of its prime factors. Breaking a number down into the product of prime factors is known as finding its prime factorization. This process is very simple and in most cases, one can use a visual aid such as a factor tree or division ladder.

Prime Factorization of a Number:

- Start with any two factors of the number
- For each factor, we check to see if the number is prime, circle any prime factor(s) and stop working on that/those numbers
- For factors that are composite, we repeat the process and find any two factors
- This process continues until all factors are prime
- The circled numbers represent the prime factors of the number

Start with any 2 factors of the number: 120 = 60 x 2

Check to see if either factor is prime: 60 is not prime, 2 is prime

Circle 2 and continue working on 60

120 = 60 x 2

Repeat the process on 60, find any 2 factors: 60 = 30 x 2

Check to see if either factor is prime: 30 is not prime, 2 is prime

Circle 2 and continue working on 30

120 = 30 x 2 x 2

Repeat the process on 30, find any 2 factors: 30 = 15 x 2

Check to see if either factor is prime: 15 is not prime, 2 is prime

Circle 2 and continue working on 15

120 = 15 x 2 x 2 x 2

Repeat the process on 15, find any 2 factors: 15 = 5 x 3

Check to see if either factor is prime: 5 is prime, 3 is prime

Circle 5 and 3, we have found our prime factorization:

120 = 5 x 3 x 2 x 2 x 2

Prime Factorization Resources:

Videos:

Khan Academy - Video Virtual Nerd - Video Krista King - YouTube - Video Text Lessons:

Math is Fun - Text Lesson Cool Math - Text Lesson Chili Math - Text Lesson Worksheets:

K5 Learning - Worksheet Dads Worksheets - Worksheet Khan Academy - Practice + Show More +