1. Homework Expectations
Warm Up
Homework Expectations
Lesson Presentation
Exit Ticket

2. Warm Up
List 6 different prime numbers.
Prime numbers are numbers that can only be divided by itself and one.

3. Ms. Ryan’s Homework Expectations
Write your name, date and period on the top of EVERY paper.
Write the page number at the beginning of each new section.
Write the problem number next to your answer.
Show your work!!!

4. Example:
Ms. Ryan
1/19/12
Pd. 6
Page 523 1. 2.
Page 598

5. 4-1 Greatest Common Factor
Goal: Learn how to find the greatest common factor of two or more numbers.

6. Vocabulary
greatest common factor (GCF)

7. 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:
List all the factors of each number
Use prime factorization

8. Example 1: Using a List to Find the GCF
Find the greatest common factor (GCF) of 12, 36, 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 GCF is 6.

9. 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
List all of the factors of each number.
Circle the greatest factor that is in all the lists.
The GCF is 7.

10. Vocabulary
prime factorization

11. 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

12. Example 3: Using Prime Factorization to Find the GCF
Find the greatest common factor (GCF).
40, 56
Write the prime factorization of
each number and circle the
common prime factors.
40 = 2 · 2 · 2 · 5
56 = 2 · 2 · 2 · 7
2 · 2 · 2 = 8
Multiply the common prime factors.
The GCF is 8.

13. Example 4: Using Prime Factorization to Find the GCF
Find the greatest common factor (GCF).
252, 180, 96, 60
Write the prime factorization
of each number and circle
the common prime factors.
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
Multiply the common prime
factors.
The GCF is 12.

14. On Your Own: Example 5
Find the greatest common factor (GCF).
72, 84
72 = 2 · 2 · 2 · 3 · 3
Write the prime factorization of each number and circle the common prime factors.
84 = 2 · 2 · 7 · 3
2 · 2 · 3 = 12
Multiply the common prime factors.
The GCF is 12.

15. Find the greatest common factor (GCF).
On Your Own: Example 6
Find the greatest common factor (GCF).
360, 250, 170, 40
360 = 2 · 2 · 2 · 3 · 3 · 5
Write the prime factorization
of each number and circle the common prime factors.
250 = 2 · 5 · 5 · 5
170 = 2 · 5 · 17
40 = 2 · 2 · 2 · 5
2 · 5 = 10
Multiply the common prime
factors.
The GCF is 10.

16. Example 7: Word Problem
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?

17. Understand the Problem
Example 7 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 GCF of 120, 100, and 45.

18. Example 7 Continued 2
Make a Plan
You can list the prime factors of 120, 100,
and 45 to find the GCF.
Solve 3
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.

19. Example 7 Continued
Look Back 4
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with nothing left over.

20. 4-5 Least Common Multiple
Goal: Learn how to find the least common multiple of two or more numbers.

21. Vocabulary
multiple
common multiple
least common multiple

22. A multiple of a number is a product of that number and a whole number
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.

27. Understand the Problem
Check It Out: Example 3 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 GCF of 24 and 18.

28. Check It Out: Example 3 Continued2
Make a Plan
You can list the prime factors of 24 and 18
to find the GCF.
Solve 3
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
Multiply the prime factors that are common to both 24 and 18.
2 · 3 = 6
You can make 6 sets of flies.

29. Check It Out: Example 3 Continued
Look Back 4
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.

30. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

31. Lesson Quiz: Part I
Find the greatest common factor (GCF).
1. 28, 40
2. 24, 56
3. 54, 99
4. 20, 35, 70 4 8 9 5

32. 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

33. Lesson Quiz for Student Response Systems
1. Identify the greatest common factor (GCF) of 49 and 63.
A. 6
B. 7
C. 8
D. 9

34. Lesson Quiz for Student Response Systems
2. Identify the greatest common factor (GCF) of 25 and 15.
A. 8
B. 6
C. 5
D. 4

35. Lesson Quiz for Student Response Systems
3. Identify the greatest common factor (GCF) of 32 and 40.
A. 3
B. 4
C. 6
D. 8

36. Lesson Quiz for Student Response Systems
4. Identify the greatest common factor (GCF) of 24, 16, and 32.
A. 4
B. 6
C. 8
D. 9

37. Lesson Quiz for Student Response Systems
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