Transcript greatest common divisor (GCD)

3-2 Greatest Common Divisor
California
Standards
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).
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
Teacher Example 1: Using a List to Find the GCD
Find the greatest common divisor (GCD) of 12,
36, and 54.
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
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
The GCD is 6.
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
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
The GCD is 7.
Holt CA Course 1
3-2 Greatest Common Divisor
Teacher Example 2: Problem Solving Application
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?
Holt CA Course 1
3-2 Greatest Common Divisor
Teacher Example 2 Continued:
1
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
Teacher Example 2 Continued:
2
Make a Plan
You can list the prime factors of 120, 100,
and 45 to find the GCD.
3
Solve
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.
Holt CA Course 1
3-2 Greatest Common Divisor
Teacher Example 2 Continued:
4
Look Back
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with no beads left over.
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 Divisor
Student Practice 2 Continued:
1
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
Student Practice 2 Continued:
2
Make a Plan
You can list the prime factors of 24 and 18
to find the GCD.
3
Solve
24 = 2  2  2  3
18 = 2  3  3
Multiply the prime factors
23=6
that are common to both
24 and 18.
You can make 6 sets of flies.
Holt CA Course 1
3-2 Greatest Common Divisor
Student Example 2 Continued:
4
Look Back
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.
Holt CA Course 1
3-2 Greatest Common Divisor
Lesson Quiz
Find the greatest common divisor (GCD).
1. 28, 40 4
2. 24, 56
3. 54, 99 9
4. 20, 35, 70 5
8
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
Holt CA Course 1