Greatest Common Factor and Prime Factorization

Greatest Common Factor

(GCF)

Multiple Choice

What is a factor?

• Numbers

• Numbers multiplied to equal a product

• Prime numbers

Multiple Select

How can you list all of the factors?

• Factor Tree Method

• Rainbow Factor Method

• List Multiplication Factors Method

are whole numbers that can be multiplied together to equal a product

Factors:

​Each branch of the tree is split into factors. Expresses the prime factorization of a number.

​​Factor Tree

​List all of the possible factors that multiply to equal the product.

​​Rainbow Factors:

Factors

An integer that's greater than 1 will always have at least two factors:

1 and itself

Many numbers have several factors. 

For example, the number 20 has

six different factors.

Multiple Choice

What does GCF stand for?

• Greatest Common Factor

• Good Clean Fun

• General Collateral Financing

Factors of 8:

1, 2, 4, 8

Factors of 12:

1, 2, 3, 4, 6, 12

Largest factor they BOTH have in common is 4. This means 4 is the largest number that will divide evenly into 8 and 12.

EXAMPLE: GCF for 8 and 12

is the largest number that is a factor of two or more numbers. 

It's the biggest number that will divide evenly into the numbers given.

​Commonly referred to as a GCF:

Greatest Common Factor (GCF)

Open Ended

How do you find the Greatest Common Factor?

Use this method if numbers are large. Use a factor tree. List all the prime factors (even if the numbers repeat). Multiply the common prime factors to figure out the GCF.

2. Prime Factorization

List the factors of each number.

Circle the largest common factor.

​1. List Factors

Two Methods

Open Ended

How will finding the GCF help me in this class?