Homework Expectations Warm Up Homework Expectations Lesson Presentation Exit Ticket

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 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!!!

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

4-1 Greatest Common Factor 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: List all the factors of each number Use prime factorization

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.

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.

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

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.

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.

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.

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.

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?

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.

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.

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.

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 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.

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.

Check It Out: Example 3 Continued 2 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.

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.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

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

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

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

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

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

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