06 GCF Greatest Common Factor GCF Greatest means _________ Biggest, Largest, Highest Common means ________ Share, have the same, be alike A Factor is _________ Two numbers that can be multiplied together to get another number … 10 ÷ 5 = 2 so 5 and 2 are factors of 10

The greatest common factor of two or more numbers is the greatest number that is a factor of every number.

There’s 3 ways to Find GCF Make a list of all the factors (rainbow) Use Prime Factors (Ladder method) Use Prime Factors (Venn Diagram method)

Method 1: Making a List Step 1: Find all the factors of both numbers Example: ALWAYS start with 1 x ____ 1 x 12 2 x __ use divisibility rules…does 2 work? 3 x __ use divisibility rules…does 3 work? We are DONE cuz 3 & 4 are right next to each other!! 6 4

18 Let’s find all the factors of 18 ALWAYS start with 1 x ____ 1 x 18 2 x __ use divisibility rules…does 2 work? 3 x __ use divisibility rules…does 3 work? 4 x __ …does 4 work? 5 x __ use divisibility rules…does 5 work? We are DONE cuz 3,4,5, 6 … 6 is already on the list so we are working back up. 18 9 6 No No

How do we know when we are DONE? 1 x 12 = 2 6 3 4 5 2.4 7 1.7 8 1.5 9 1.3 10 1.2 11 1.1 1 x 12 2 x 6 3 x 4

Step 2: List all Factors in a list 1 x 12 2 x 6 3 x 4 12: 1, 2, 3, 4, 6, 12

Step 3: Find the largest factor both numbers have in common. 12: 1, 2, 3, 4, 6, 12 What one is the Greatest? 18: 1, 2, 3, 6, 9, 18

Method 2: Ladder Method (Prime Factorization) is a method of factoring which allows you to factor two numbers at once Step 1: List each number in the ladder Example:

Step 2: Factor using a prime number such as 2, 3, 5, or 7 Example:

Step 3: Multiply the numbers on the outside of the ladder to get the GCF. Example:

Method 3: Venn Diagram Method (Prime Factorization) Step 2: Circle all of the PRIME factors. Example: Step 1: Create factor trees for both numbers. Example:

Step 3: Place each prime factor that both numbers have in common in the center part of this Venn Diagram. Example:

Step 4: Multiply the numbers in the middle to get the GCF, if needed. Example: **The numbers left in the top and bottom are simplified when reducing fractions.

Let’s Try Some Find the GCF for 4 and 8 Find the GCF for 12 and 20