06 GCF Greatest Common Factor GCF Greatest means

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

There’s 3 ways to Find GCF 1) Make a list of all the factors

Method 1: Making a List Step 1: Find all the factors of both numbers

Let’s find all the factors of 18 ALWAYS start with 1 x ____ 1

How do we know when we are DONE? 1 x 12 2 x 6

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

Step 3: Find the largest factor both numbers have in common. What one is

Method 2: Ladder Method (Prime Factorization) • is a method of factoring which allows

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

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

Method 3: Venn Diagram Method (Prime Factorization) • Step 1: Create factor trees for

Step 3: Place each prime factor that both numbers have in common in the

Step 4: Multiply the numbers in the middle to get the GCF, if needed.

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

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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 1) Make a list of all the factors (rainbow) 2) Use Prime Factors (Ladder method) 3) 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!!

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.

How do we know when we are DONE? 1 x 12 2 x 6 3 x 4 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 4 x 3 = 12 5 x 2. 4 = 12 6 x 2 = 12 7 x 1. 7 = 12 8 x 1. 5 = 12 9 x 1. 3 = 12 10 x 1. 2 = 12 11 x 1. 1 = 12 12 x 1 = 12

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. What one is the Greatest? 12: 1, 2, 3, 4, 6, 12 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 1: Create factor trees for both numbers. Example: • Step 2: Circle all of the PRIME factors. 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 • Find the GCF for 21 and 3 • Find the GCF for 28 and 12 • Find the GCF for 90 and 30