1. Name ______________________________ Date ___________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 3Greatest Common Factor
TB 4-3 / OC 1-6
Essential Question: Why is it important to have strategies to manipulate numbers?
VOCABULARY DEFINTION EXAMPLE
Common Factor
Greatest Common
Factor (GCF)
Method 1 – List Method.
16: 1, 2, 4, 8 , 16
1. List all the factors of both numbers
24: 1, 2, 3, 4, 6, 8, 12, 24
2. Look for the largest factor that both 16: 1, 2, 4, 8 , 16
numbers have in common. 24: 1, 2, 3, 4, 6, 8, 12, 24
3. Find the Greatest Common Factor The GCF of 16 and 24 is 8.
What divisibility
Find the GCF of each set of numbers using the list method. rules can help you?
____
(draw the factor trees – it will be very helpful!!!!)
1. 32 and 48 2. 45 and 81 3. 18 and 36
32 _____________ 45 _____________ 18 _____________
48 _____________ 81 _____________ 36 _____________
GCF:___________ GCF:___________ GCF:___________

2. Method 2: Prime Factorization to find the GCF.
Write the prime factorization of both numbers.
1. Write the prime factorization of each 16: 2 • 2 • 2 • 2
number. (Do not write in exponential form.) 24: 2 • 2 • 2 • 3
Use scrap paper
16: 2 • 2 • 2 • 2
2. Find the common prime factors.
24: 2 • 2 • 2 • 3
3. Find the product of the common 2 •2 •2 = 8
prime factors. The GCF of 16 and 24 is 8.
What divisibility
Now you try some: rules can help you?
____
(draw the factor trees – it will be very helpful!!!!)
1. 6 and 9 2. 4 and 8 3. 8 and 12
6 _____________ 4_____________ 8_____________
9 _____________ 8_____________ 12_____________
GCF: _________ GCF:__________ GCF:__________
4. 6 and 15 5. 10 and 15 6. 9 and 12
6 _____________ 10_____________ 9_____________
15 _____________ 15_____________ 12_____________
GCF: _________ GCF:__________ GCF:__________

3. Name ______________________________ Date ___________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 3Greatest Common Factor
TB 4-3 / OC 1-6
Essential Question: Why is it important to have strategies to manipulate numbers?
VOCABULARY DEFINTION EXAMPLE
Factors of 12:
1,2,3,4,6,12
Factors shared by
Factors of 18:
Common Factor two or more whole
1,2,3,6,9,18
numbers
Common Factors:
1,2,3,6
The largest of the
Common Factors:
common factors
Greatest Common 1,2,3,6
shared by two or
Factor (GCF) 6 is the Greatest
more whole
Common Factor
numbers
Method 1 – List Method.
16: 1, 2, 4, 8 , 16
4. List all the factors of both numbers
24: 1, 2, 3, 4, 6, 8, 12, 24
5. Look for the largest factor that both 16: 1, 2, 4, 8 , 16
numbers have in common. 24: 1, 2, 3, 4, 6, 8, 12, 24
6. Find the Greatest Common Factor The GCF of 16 and 24 is 8.
What divisibility
Find the GCF of each set of numbers using the list method. rules can help you?
1. 32 and 48 2. 45 and 81 3. 18 and 36 ____
32 1,2,4,8,16,32 451,3,5,9,15,45 18 1,2,3,6,9,18
48 1,2,3,4,6,8,12,16,24,48 81 1,3,9,27,81 36 1,2,3,4,6,9,12,18,36
GCF: 16 GCF: 9 GCF: 18
Method 2: Prime Factorization to find the GCF.

4. Write the prime factorization of both numbers.
2. Write the prime factorization of each 16: 2 • 2 • 2 • 2
number. (Do not write in exponential form.) 24: 2 • 2 • 2 • 3
Use scrap paper
16: 2 • 2 • 2 • 2
2. Find the common prime factors.
24: 2 • 2 • 2 • 3
3. Find the product of the common 2 •2 •2 = 8
prime factors. The GCF of 16 and 24 is 8.
Now you try some: (draw the factor trees – it will be very helpful!!!!)
What divisibility
1. 6 and 9 2. 4 and 8 3. 8 and 12 rules can help you?
____
62•3 4 2 •2 8 2 •2 •2
93•3 8 2 •2 •2 12 2 •2 •3
2 •2 2 •2
GCF: 3 GCF: 4 GCF: 4
4. 6 and 15 5. 10 and 15 6. 9 and 12
6 2•3 10 2 • 5 9 3 • 3
15 3•5 15 3 • 5 12 2 •2 •3
GCF: 3 GCF: 5 GCF: 3

5. #1-3 Use List Method
#4-6 Use Prime Factorization Method
#7-9 do NOT do