1. Greatest Common Factor (GCF)

2. Standard
M6N1 Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.
b. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.

3. How are GCF and LCM applied to fractions?
Essential Questions
How are GCF and LCM applied to fractions?

4. The GCF of two or more numbers is the greatest number that is a factor of each number

5. 1) Listing the Factors 2) Prime Factorization 3) Ladder method
Three ways to find GCF:
1) Listing the Factors
2) Prime Factorization
3) Ladder method

6. Step 1: List the factors of the numbers
1) Listing the Factors
Step 1: List the factors of the numbers

7. Example: 24 and 36 36 24
3 8
4 6
4 9
6 6

8. Step 2: List the common factors (the numbers that are in both lists).

9. Common Factors of 24 & 36 are:
1, 2, 3, 4, 6, 12

10. The largest is the greatest common factor:12

11. Step 1: For each number draw a factor tree
2) Prime Factorization
Step 1: For each number draw a factor tree

12. Example: 24 and 36 36 24
4 6
6 6
2 3
2 2
2 3
2 3 12 • • 2 2 3 =

13. Using the Prime Factorization Method:
The GCF is also 12

14. 3) Ladder method

15. Multiply all common factors from outside of divided by box
Multiply all common factors from outside of divided by box. 2 x 2 x 2 x 6 x 1= GCF 48

16. Find the Greatest Common Factor for the following:
1) 8 and 24
2) 15 and 45

17. Answers
1) GCF is 8
2) GCF is 15

18. Find the GCF
36 and 54
72 and 120
14 and 33
108 and 132