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Greatest Common
Factor (GCF)
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
Common Core Objective:
Students will be able to identify the greatest common
factors of two or three one, two, and three digit
numbers with 80% accuracy.
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.
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
Greatest Common Factor (GCF)
But if that’s too hard…
Simply THINK
G…Greatest (largest)
C…Common (shared)
F…Factor
Greatest Common Factor (GCF)
Important to Remember…
TWO
There are
methods for finding
the GCF of two or more numbers…
Method 1…Use Book Ends
Method 2…Use Prime Factorization
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
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
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
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
2
12
2 6
2 3
2·2·2·3
36
2
12
2 6
3 3
2·2·3·3
24: 2 · 2 · 2 · 3
36: 2 · 2 · 3 · 3
2 · 2 · 3 = 12
GCF = 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
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
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
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
2
24
6
2 3
2·2·3
2
12
2 6
2 3
2·2·3·3
12: 2 · 2 · 3
24: 2 · 2 · 2 · 3
2 · 2 · 3 = 12
GCF = 12
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
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
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
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
2
20
8
2 4
2 2
2·2·2·2
2
10
2 5
2·2·5
16: 2 · 2 · 2 · 2
20: 2 · 2 · 5
2·2=4
GCF = 4
Greatest Common Factor (GCF)
Important to Remember…
TWO
There are
methods for finding
the GCF of two or more numbers…
Method 1…Use Book Ends
Method 2…Use Prime Factorization
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
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
=> 3
=> 6
=> 16
4. 40a2b, 48ab4
=> 8ab
Greatest Common Factor (GCF)
Homework
p.162 #20-30, even,
34, 36