2-5 greatest common factor course 2 warm up warm up problem of the day problem of the day lesson...
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2-5 Greatest Common Factor
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpWrite the prime factorization of each number.
1. 20
2. 100
3. 30
4. 128
5. 70
22 · 5
22 · 52
2 · 3 · 5
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2-5 Greatest Common Factor
27
2 · 5 · 7
Problem of the Day: Part 1
Use the clues to find the numbers being described.
1. a. The greatest common factor (GCF) of two numbers is 5.
b. The sum of the numbers is 75. c. The difference between the
numbers is 5. 35 and 40
Course 2
2-5 Greatest Common Factor
Problem of the Day: Part 2
Use the clues to find the numbers being described.2. a. The GCF of three different numbers is 4. b. The sum of the numbers is 64.
Possible answer: 12, 16, 36
Course 2
2-5 Greatest Common Factor
Learn to find the greatest common factor of two or more whole numbers.
Course 2
2-5 Greatest Common Factor
Vocabulary
greatest common factor (GCF)
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Course 2
2-5 Greatest Common Factor
Course 2
2-5 Greatest Common Factor
The greatest common factor (GCF) of two or more whole numbers is the greatest whole number that divides evenly into each number.
One way to find the GCF of two or more numbers is to list all the factors of each number. The GCF is the greatest factor that appears in all the lists.
Find the greatest common factor (GCF).
Additional Example 1: Using a List to Find the GCF
Course 2
2-5 Greatest Common Factor
12, 36, 54
12: 1, 2, 3, 4, 6, 12
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
54: 1, 2, 3, 6, 9, 18, 27, 54
The GCF is 6.
List all of the factors of each number.
Circle the greatest factor that is in allthe lists.
Try This: Example 1
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2-5 Greatest Common Factor
Find the greatest common factor (GCF).
14, 28, 63
14: 1, 2, 7, 14
28: 1, 2, 4, 7, 14, 28
63: 1, 3, 7, 9, 21, 63
The GCF is 7.
List all of the factors ofeach number.
Circle the greatest factor that is in allthe lists.
Find the greatest common factor (GCF).
Additional Example 2A: Using Prime Factorization to Find the GCF
Course 2
2-5 Greatest Common Factor
A. 40, 56
40 = 2 · 2 · 2 · 5
56 = 2 · 2 · 2 · 7
2 · 2 · 2 = 8
The GFC is 8.
Write the prime factorization of each number and circle the common factors.
Multiply the common prime factors.
Find the greatest common factor (GCF).
Additional Example 2B: Using Prime Factorization to Find the GCF
Course 2
2-5 Greatest Common Factor
B. 252, 180, 96, 60
252 = 2 · 2 · 3 · 3 · 7
180 = 2 · 2 · 3 · 3 · 5
96 = 2 · 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
2 · 2 · 3 = 12
The GCF is 12.
Write the prime factorizationof each number and circlethe common prime factors.
Multiply the common primefactors.
Try This: Example 2A
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2-5 Greatest Common Factor
Find the greatest common factor (GCF).
A. 72, 84
72 = 2 · 2 · 2 · 9
84 = 2 · 2 · 7 · 3
2 · 2 = 4
The GCF is 4.
Write the prime factorization of each number and circle the common factors.Multiply the common prime factors.
Try This: Example 2B
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2-5 Greatest Common Factor
Find the greatest common factor (GCF).
B. 360, 250, 170, 40
360 = 2 · 2 · 2 · 9 · 5
250 = 2 · 5 · 5 · 5
170 = 2 · 5 · 17
40 = 2 · 2 · 2 · 5
2 · 5 = 10
The GCF is 10.
Write the prime factorizationof each number and circlethe common prime factors.
Multiply the common primefactors.
You have 120 red beads, 100 white beads, and 45 blue beads. You want to use all the beads to make bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make?
Additional Example 3: Problem Solving Application
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2-5 Greatest Common Factor
Additional Example 3 Continued
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2-5 Greatest Common Factor
11 Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of matching bracelets you can make.
List the important information:
• There are 120 red beads, 100 white beads, and 45 blue beads.
• Each bracelet must have the same number of red, white, and blue beads.
The answer will be the GCF of 120, 100, and 45.
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2-5 Greatest Common Factor
22 Make a Plan
You can list the prime factors of 120, 100,and 45 to find the GFC.
Solve33
120 = 2 · 2 · 2 · 3 · 5
100 = 2 · 2 · 5 · 5
45 = 3 · 3 · 5
The GFC of 120, 100, and 45 is 5.
You can make 5 bracelets.
Additional Example 3 Continued
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2-5 Greatest Common Factor
Look Back44
If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 bluebeads, with nothing left over.
Additional Example 3 Continued
Try This: Example 3
Nathan has made fishing flies that he plans to give away as gift sets. He has 24 wet flies and 18 dry flies. Using all of the flies, how many sets can he make?
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2-5 Greatest Common Factor
Try This: Example 3 Continued
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2-5 Greatest Common Factor
11 Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of sets of flies he can make.
List the important information:
• There are 24 wet flies and 18 dry flies. • He must use all of the flies.
The answer will be the GCF of 24 and 18.
Course 2
2-5 Greatest Common Factor
22 Make a Plan
You can list the prime factors of 24 and 18 to find the GCF.
Try This: Example 3 Continued
Solve33
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
You can make 6 sets of flies.
2 · 3 = 6Multiply the prime factors that are common to both 24 and 18.
Try This: Example 3 Continued
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2-5 Greatest Common Factor
Look Back44
If you make 6 sets, each set will have 3 dry flies and 4 wet flies.
Lesson Quiz: Part 1
Find the greatest common factor (GCF).
1. 28, 40
2. 24, 56
3. 54, 99
4. 20, 35, 70
8
4
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9
5
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2-5 Greatest Common Factor
Lesson Quiz: Part 2
5. The math clubs from 3 schools agreed to a competition. Members from each club must be divided into teams, and teams from all clubs must be equally sized. What is the greatest number of members that can be on a team if Georgia has 16 members, William has 24 members, and Fulton has 72 members?
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2-5 Greatest Common Factor
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