1. Greatest Common Factor (GCF)

2. Greatest Common Factor (GCF)
Essential Question:
How do I find the greatest common factor of two or three numbers, and why is this relevant to me?
Common Core Objective:
6.NS.4
Students will be able to identify the greatest common factors of two or three one, two, and three digit numbers with 80% accuracy.

3. Greatest Common Factor (GCF)
Vocabulary:
Factor – a number that divides into a whole number with a remainder of zero.
Greatest Common Factor – the largest factor that two or more numbers have in common.

4. Greatest Common Factor (GCF)
When thinking about finding the Greatest Common Factor, or the GCF…
THINK BACKWARDS
F…Find the Factors
C…Circle Common Factors
G…Group Largest Factor

5. Greatest Common Factor (GCF)
But if that’s too hard…
Simply THINK
G…Greatest (largest)
C…Common (shared)
F…Factor

6. Greatest Common Factor (GCF)
Important to Remember…
There are TWO methods for finding the GCF of two or more numbers…
Method 1…Use Book Ends
Method 2…Use Prime Factorization

7. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 1: Find the GCF of 24 and 36.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common

8. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 1: Find the GCF of 24 and 36.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common
24: 1, 2, 3, 4, 6, 8, 12, 24
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The GCF of 24 and 36 is 12

9. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 1: Find the GCF of 24 and 36.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors

10. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 1: Find the GCF of 24 and 36.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors 24 36
24: 2 · 2 · 2 · 3 2 12 2 12
36: 2 · 2 · 3 · 3 2 6 2 6
2 · 2 · 3 = 12 2 3 3 3
GCF = 12
2 · 2 · 2 · 3
2 · 2 · 3 · 3

11. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 2: Find the GCF of 12 and 24.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common

12. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 2: Find the GCF of 12 and 24.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common
12: 1, 2, 3, 4, 6, 12
24: 1, 2, 3, 4, 6, 8, 12, 24
The GCF of 12 and 24 is 12

13. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 2: Find the GCF of 12 and 24.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors

14. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 2: Find the GCF of 12 and 24.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors 12 24
12: 2 · 2 · 3 2 6 2 12
24: 2 · 2 · 2 · 3 2 3 2 6
2 · 2 · 3 = 12 2 3
GCF = 12
2 · 2 · 3
2 · 2 · 3 · 3

15. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 3: Find the GCF of 16 and 20.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common

16. Greatest Common Factor (GCF)
Finding the GCF: Method 1 – Book Ends
Example 3: Find the GCF of 16 and 20.
Step 1: Find the factors of each number.
Step 2: Circle the common factors of the numbers
Step 3: Group or circle the largest factor they have in common
16: 1, 2, 4, 8, 16
20: 1, 2, 4, 5, 10, 20
The GCF of 16 and 20 is 4

17. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 3: Find the GCF of 16 and 20.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors

18. Greatest Common Factor (GCF)
Finding the GCF: Method 2 – Prime Factorization
Example 3: Find the GCF of 16 and 20.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of the common prime factors 16 20
16: 2 · 2 · 2 · 2 2 8 2 10
20: 2 · 2 · 5 2 4 2 5
2 · 2 = 4 2 2
GCF = 4
2 · 2 · 2 · 2
2 · 2 · 5

19. Greatest Common Factor (GCF)
Important to Remember…
There are TWO methods for finding the GCF of two or more numbers…
Method 1…Use Book Ends
Method 2…Use Prime Factorization

20. Greatest Common Factor (GCF)
Guided Practice Problems
Directions: Find the GCF of each set of numbers.
1. 9, 12, 30
2. 42, 60
3. 48, 64
4. 40a2b, 48ab4

21. Greatest Common Factor (GCF)
Guided Practice Problems
Directions: Find the GCF of each set of numbers.
1. 9, 12, 30 => 3
2. 42, 60 => 6
3. 48, 64 => 16
4. 40a2b, 48ab4 => 8ab

22. Greatest Common Factor (GCF)
Homework
p.162 #20-30, even,
34, 36