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Holt CA Course 1
3-2 Greatest Common Divisor
NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction).
California Standards
Holt CA Course 1
3-2 Greatest Common Divisor
VOCABULARY CARDS
• Divisor
• Greatest Common Divisor (GCD)
Holt CA Course 1
3-2 Greatest Common Divisor
The greatest common divisor (GCD) of two or more whole numbers is the greatest whole number that divides evenly into each number.
One way to find the GCD of two or more numbers is to list all the factors of each number. The GCD is the greatest factor that appears in all the lists.
Holt CA Course 1
3-2 Greatest Common Divisor
Find the greatest common divisor (GCD) of 12, 36, and 54.
Teacher Example 1: Using a List to Find the GCD
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The GCD is 6.
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
Holt CA Course 1
3-2 Greatest Common Divisor
Student Practice 1:
Find the greatest common divisor of 14, 28, and 63.
14: 1, 2, 7, 14
28: 1, 2, 4, 7, 14, 28
63: 1, 3, 7, 9, 21, 63
The GCD is 7.
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
Holt CA Course 1
3-2 Greatest Common Divisor
You have 120 red beads, 100 white beads, and 45 blue beads. You want to use all the beads to make identical bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make?
Teacher Example 2: Problem Solving Application
Holt CA Course 1
3-2 Greatest Common DivisorTeacher Example 2 Continued:
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 GCD of 120, 100, and 45.
Holt CA Course 1
3-2 Greatest Common Divisor
22 Make a Plan
You can list the prime factors of 120, 100,and 45 to find the GCD.
Solve33
120 = 2 2 2 3 5
100 = 2 2 5 5
45 = 3 3 5
The GCD of 120, 100, and 45 is 5.
You can make 5 bracelets.
Teacher Example 2 Continued:
Holt CA Course 1
3-2 Greatest Common Divisor
Look Back44
If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 bluebeads, with no beads left over.
Teacher Example 2 Continued:
Holt CA Course 1
3-2 Greatest Common Divisor
Student Practice 2:
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?
Holt CA Course 1
3-2 Greatest Common DivisorStudent Practice 2 Continued:
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 GCD of 24 and 18.
Holt CA Course 1
3-2 Greatest Common Divisor
22 Make a Plan
You can list the prime factors of 24 and 18 to find the GCD.
Student Practice 2 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.
Holt CA Course 1
3-2 Greatest Common Divisor
Student Example 2 Continued:
Look Back44
If you make 6 sets, each set will have 3 dry flies and 4 wet flies.
Holt CA Course 1
3-2 Greatest Common DivisorLesson Quiz
Find the greatest common divisor (GCD).
1. 28, 40 2. 24, 56
3. 54, 99 4. 20, 35, 70
84
9 5
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, Williams has 24 members, and Fulton has 72 members? 8