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Warm Up Write the prime factorization of each number. 1. 14 3. 63 2. 18 4. 54

Warm Up Write the prime factorization of each number. 1. 14 3. 63 2. 18 4. 54

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## Warm Up Write the prime factorization of each number. 1. 14 3. 63 2. 18 4. 54

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**Warm Up**Write the prime factorization of each number. 1. 14 3. 63 2. 18 4. 54 2 7 32 7 2 33 2 32**Greatest Common Factor (GCF)- the largest of the common**factors shared.. Factors of 24: Factors of 36: Common factors: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 12 GCF = 12**Ex. 1**Find the GCF of the set of numbers. 28 and 42 Method 1: List the factors. factors of 28: factors of 42: List all the factors. 1, 2, 4, 7, 14, 28 1, 2, 3, 6, 7, 14, 21, 42 Circle the GCF. The GCF of 28 and 42 is 14.**Ex. 2**Find the GCF of the set of numbers. 18 and 36 Method 1: List the factors. factors of 18: factors of 36: List all the factors. 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 6, 9, 12, 18, 36 Circle the GCF. The GCF of 18 and 36 is 18.**Ex. 3**Find the GCF of the set of numbers. 18, 30, and 24 Method 2: Use the prime factorization. 18 = 30 = 24 = 2 • 3 • 3 Write the prime factorization of each number. 2 • 3 • 5 2 • 3 • 2 • 2 Find the common prime factors. Find the prime factors common to all the numbers. 2• 3 = 6 The GCF of 18, 30, and 24 is 6.**Ex. 4**Find the GCF of the set of numbers. 10, 20, and 30 Method 2: Use the prime factorization. 10 = 20 = 30 = 2 • 5 Write the prime factorization of each number. 2 • 5 • 2 2 • 5 • 3 Find the common prime factors. Find the prime factors common to all the numbers. 2• 5 = 10 The GCF of 10, 20, and 30 is 10.**45 18 27**15 6 9 Ex. 5 Find the GCF of the set of numbers. 45, 18, and 27 Method 3: Use a ladder diagram. 3 Begin with a factor that divides into each number. Keep dividing until the three have no common factors. 3 5 2 3 Find the product of the numbers you divided by. 3• 3 = 9 The GCF of 45, 18, and 27 is 9.**40 16 24**20 8 12 10 4 6 Ex. 6 Find the GCF of the set of numbers. 40, 16, and 24 Method 3: Use a ladder diagram. 2 Begin with a factor that divides into each number. Keep dividing until the three have no common factors. 2 2 5 2 3 Find the product of the numbers you divided by. 2• 2• 2= 8 The GCF of 40, 16, and 24 is 8.**Ex. 7**Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make?**1**Understand the Problem 2 Make a Plan Ex. 7 continued The answer will be the greatest number of fruit baskets 18 oranges and 27 pears can form so that each basket has the same number of oranges, and each basket has the same number of pears. You can make an organized list of the possible fruit baskets.**3**Solve Oranges Pears Bouquets 2 3 OO PPP OO PPP OO PPP OO PPP OO PPP OO PPP OO PPP OO PPP OO PPP 4 18 oranges, 27 pears: Every fruit is in a basket The greatest number of baskets Peter can make is 9. Look Back To form the largest number of baskets, find the GCF of 18 and 27. factors of 18: factors of 27: 1, 9, 6, 18 2, 3, 1, 3, 9, 27 The GCF of 18 and 27 is 9.**Lesson Quizzes**Standard Lesson Quiz Lesson Quiz for Student Response Systems**Lesson Quiz: Part I**Find the greatest common factor of each set of numbers. 1. 18 and 30 2. 20 and 35 3. 8, 28, 52 4. 44, 66, 88 6 5 4 22**Lesson Quiz: Part II**Find the greatest common factor of the set of numbers. 5. Mrs. Lovejoy makes flower arrangements. She has 36 red carnations, 60 white carnations, and 72 pink carnations. Each arrangement must have the same number of each color. What is the greatest number of arrangements she can make if every carnation is used? 12 arrangements**Lesson Quiz for Student Response Systems**1. Identify the greatest common factor of 28 and 36. A. 2 B. 4 C. 6 D. 7**Lesson Quiz for Student Response Systems**2. Identify the greatest common factor of 49 and 77. A. 3 B. 5 C. 7 D. 11**Lesson Quiz for Student Response Systems**3. Identify the greatest common factor of 16, 24, and 40. A. 2 B. 4 C. 5 D. 8**Lesson Quiz for Student Response Systems**4. Identify the greatest common factor of 42, 63, and 84. A. 3 B. 7 C. 19 D. 21**Lesson Quiz for Student Response Systems**5. Harry collected 42 first-aid kits, 56 blankets, and 70 food packets for a flood-relief camp. He wants to pack the collected items in boxes in such a way that each box has the same number of items of each kind. What is the greatest number of boxes that Harry needs? A. 7 boxes B. 14 boxes C. 21 boxes D. 24 boxes