1. 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

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

4. 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)

5. 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

6. 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

7. 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

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

9. 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

10. 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:

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

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

13. 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:

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

15. 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.

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