2-7 Greatest Common Factor Warm Up Warm Up Lesson Presentation Lesson Presentation Homework Expectations Exit Ticket Exit Ticket

2-7 Greatest Common Factor

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Lesson Presentation

Homework Expectations

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Warm Up

List 6 different prime numbers.

Prime numbers are numbers that can only be divided by itself and one.


Ms. Ryan’s Homework Expectations

1.Write your name, date and period on the top of EVERY paper.2.Write the page number at the beginning of each new section.3.Write the problem number next to your answer.4.Show your work!!!


Example:Ms. Ryan

1/19/12Pd. 6

Page 5231.2.Page 5981.2.



Goal: Learn how to find the greatest common factor of two or more numbers.


Vocabulary

greatest common factor (GCF)


The greatest common factor (GCF) of two or more whole numbers is the greatest whole number that divides evenly into each number.

There are two ways to figure out the GCF:

1.List all the factors of each number

2.Use prime factorization


Find the greatest common factor (GCF) of 12, 36, 54.

Example 1: Using a List to Find the GCF

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 GCF is 6.

List all of the factors of each number.

Circle the greatest factor that is in all the lists.


On Your Own: Example 2

Find the greatest common factor of 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 of each number.

Circle the greatest factor that is in all the lists.


Vocabulary

prime factorization


Prime factorization is a composite number expressed as a product of prime numbers.

Example 1: 12 = 2 x 2 x 3

Example 2: 18 = 2 x 3 x 3

Example 3: 30 = 2 x 3 x 5


Find the greatest common factor (GCF).

Example 3: Using Prime Factorization to Find the GCF

40, 56

40 = 2 · 2 · 2 · 5

56 = 2 · 2 · 2 · 7

2 · 2 · 2 = 8

The GCF is 8.

Write the prime factorization of each number and circle the common prime factors.

Multiply the common prime factors.



Example 4: Using Prime Factorization to Find the GCF

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.




72, 84

72 = 2 · 2 · 2 · 3 · 3

84 = 2 · 2 · 7 · 3

2 · 2 · 3 = 12

The GCF is 12.

Write the prime factorization of each number and circle the common prime factors.Multiply the common prime factors.




360, 250, 170, 40

360 = 2 · 2 · 2 · 3 · 3 · 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 circle the 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?

Example 7: Word Problem


Example 7 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 GCF of 120, 100, and 45.


22 Make a Plan

You can list the prime factors of 120, 100,and 45 to find the GCF.

Solve33

120 = 2 · 2 · 2 · 3 · 5

100 = 2 · 2 · 5 · 5

45 = 3 · 3 · 5

The GCF of 120, 100, and 45 is 5.

You can make 5 bracelets.

Example 7 Continued


Look Back44

If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 bluebeads, with nothing left over.

Example 7 Continued


4-5 Least Common Multiple

Goal: Learn how to find the least common multiple of two or more numbers.


Vocabulary

multiple

common multiple

least common multiple


A multiple of a number is a product of that number and a whole number. Some multiples of 7,500 and 5,000 are as follows:

7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000, . . .

5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, . . .

A common multiple of two or more numbers is a number that is a multiple of each of the given numbers. So 15,000 and 30,000 are common multiples of 7,500 and 5,000.

2-7 Greatest Common Factor2-8 Least Common Multiple

The least common multiple (LCM) of two or more numbers is the common multiple with the least value.

Example: The LCM of 7,500 and 5,000 is 15,000.





Check It Out: Example 3 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 GCF of 24 and 18.


22 Make a Plan

You can list the prime factors of 24 and 18 to find the GCF.


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.



Look Back44

If you make 6 sets, each set will have 3 dry flies and 4 wet flies.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I


1. 28, 40

2. 24, 56

3. 54, 99

4. 20, 35, 70

8

4

9

5


Lesson Quiz: Part II

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?

8


1. Identify the greatest common factor (GCF) of 49 and 63.

A. 6

B. 7

C. 8

D. 9




A. 8

B. 6

C. 5

D. 4




A. 3

B. 4

C. 6

D. 8



4. Identify the greatest common factor (GCF) of 24, 16, and 32.

A. 4

B. 6

C. 8

D. 9



5. A florist has 20 roses, 35 lilies, and 75 daffodils. He arranges all the flowers in vases so that each vase has one type of flower and every vase has the same number of flowers. What is the greatest number of flowers in each vase?

A. 8 flowers

B. 7 flowers

C. 6 flowers

D. 5 flowers


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2-7 Greatest Common Factor Warm Up Warm Up Lesson Presentation Lesson Presentation Homework Expectations Exit Ticket Exit Ticket