1. 6.1.5 Greatest Common Factor

2. Vocabulary Common Factors – Factors shared by two or more numbers
Example: 5 is a common factor of 30 and 25
7 is a common factor of 21 and 42
Greatest Common Factor – The largest factor shared by two numbers
Example: It is true that 2 is a common factor of 16 and 24, but their GREATEST common factor is actually 8
9 is the greatest common factor of 18 and 36
12 is the greatest common factor of 24 and 48
GCF = Greatest Common Factor

3. How to Find the Greatest Common Factor?
Venn Diagram
Prime Factorization

4. Venn Diagram Example Book Something you read Movie you watch
Tells a story
Is entertaining

5. Greatest Common Factor Venn Diagram

6. Greatest Common Factor = 12 Greatest Common Factor = 15
Tables Work, Too!
Factors of ONLY 36
Factors of 36 AND 48
Factors of ONLY 48 9 18 36
12 4
3 1
Greatest Common Factor = 12 6 24 16 48
Factors of ONLY 30
Factors of 30 AND 75
Factors of ONLY 75 10
2 30
15 5 3
Greatest Common Factor = 15 75

7. Your Turn!
Factors of ONLY 16
Factors of
16 AND 56
Factors of ONLY 56

8. Greatest Common Factor = 8
Your Turn!
Factors of ONLY 16
Factors of
16 AND 56
Factors of ONLY 56 16
8 4 2
Greatest Common Factor = 8 14 56

9. Compare Three Numbers Factors of ONLY 14 Factors of ONLY 28
2 14 49
Common Factors of 14, 28, AND 49
1 and 7

10. Using Prime Factorization to Find GCF
Step #1: Draw out the prime factorization for each number
Step #2: Write out the prime factors each number has in common
Step #3: Multiply those common prime factors
Step #4: The product is the greatest common factor for the two numbers

11. Find the GCF Using Prime Factorization
12 and 56

12. Find the GCF Using Prime Factorization
12 = 4 x 3 Prime Factorization = 3 x 2 x 2 4 = 2 x 2 56 = 7 x 8 Prime Factorization = 7 x 2 x 2 x 2 8 = 2 x 4 Common Factors = 2, 2 Greatest Common Factor = 2 x 2 = 4

13. Using a Venn Diagram of Prime Factors
What two numbers does this Venn Diagram represent? 2 3
Step #1: Multiply the numbers in the first circle with the numbers in the overlapping circles (example: 2 x 3 x 3 = 18)
Step #2: Multiply the numbers in the second circle with the numbers in the overlapping cirles (example: 3 x 3 x 3 = 27) 3 3
The two numbers are 18 and 27

14. Your Turn!
2 2
3 3 11 5

15. The numbers are 180 and 55 2 2 11 3 3 5 2 x 2 x 3 x 3 x 5 = 180
2 2
3 3 11 5
2 x 2 x 3 x 3 x 5 = 180
5 x 11 = 55

16. Common Prime Factors 3 2 3 3 2 2 3 2 2 2 2 36 = 12 x 3 48 = 12 x 4
Prime Factors of ONLY 36
Common Prime Factors of 36 AND 48
Prime Factors of ONLY 48 3
3 2 2
2 2
36 = 12 x 3
12 = 4 x 3
4 = 2 x 2
36 = 3 x 3 x 2 x 2
48 = 12 x 4
12 = 4 x 3
4 = 2 x 2
48 = 3 x 2 x 2 x 2 x 2 3 2

17. How Many Gift Bags Can I Make
I went to the store to buy small gifts for the gift bags at my son’s birthday party. Unfortunately, I wasn’t able to find the same amount of each item: 18 jars of moon sand (all different colors), 24 Lego packs (all different sets), and a variety pack of Hershey’s mini chocolate bars (42 candy bars in the bag). I want identical groups of gifts in each bag with no gifts left over. What is the greatest number of gift bags I can make? 18 = 2 x 3 x 3 24 = 2 x 3 x 2 x 2 42 = 2 x 3 x 7
2 x 3 = 6 Gift Bags
Note: To find out how many of each toy should go in each bag, divide the total number of each toy by the number of gift bags you’re making. For example, of the 42 candy mini candy bars, 7 of them should be placed in each of the 6 gift bags.

18. Your Turn – Rose Bouquets
A florist is making identical bouquets using 72 red roses, 60 pink roses, and 48 yellow roses. What is the greatest number of bouquets that the florist can make if no roses are left over? How many of each color are in each bouquet?

19. Your Turn – Rose Bouquets
72 = 8 x 9 60 = 10 x 6 48 = 6 x 8 8 = 4 x 2 10 = 5 x 2 6 = 3 x 2 4 = 2 x 2 6 = 3 x 2 8 = 4 x 2 9 = 3 x 3 (5 x 2 x 3 x 2) 4 = 2 x 2 (2 x 2 x 2 x 3 x 3) (3 x 2 x 2 x 2 x 2) Common Prime Factors = 3, 2, and 2 Multiply the common prime factors: 3 x 2 x 2 = 12 Rose Bouquets 72 ÷ 12 = 6 Red Roses 60 ÷ 12 = 5 Pink Roses 48 ÷ 12 = 4 Yellow Roses

20. Homework
Page 34 (# 5, 10, 12, 15, 16, 19, 21, 24, 25, 27)