L7 b 4 3 Greatest Common Factor Warm

L-7 b 4 -3 Greatest Common Factor Warm Up Problem of the Day Lesson Presentation 6. NS. 4 Course 1

4 -3 Greatest Common Factor Warm Up Write the prime factorization of each number. 1. 14 2 7 3. 63 32 7 2. 18 2 32 4. 54 2 33 Course 1

4 -3 Greatest Common Factor Problem of the Day In a parade, there are 15 riders on bicycles and tricycles. In all, there are 34 cycle wheels. How many bicycles and how many tricycles are in the parade? 11 bicycles and 4 tricycles Course 1

4 -3 Greatest Common Factor Learn to find the greatest common factor (GCF) of a set of numbers. Course 1

4 -3 Greatest Insert Lesson Title. Factor Here Common Vocabulary greatest common factor (GCF) Course 1

4 -3 Greatest Common Factors shared by two or more whole numbers are called common factors. The largest of the common factors is called the greatest common factor, or GCF. Factors of 24: Factors of 36: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors: 1, 2, 3, 4, 6, 12 The greatest common factor (GCF) of 24 and 36 is 12. Example 1 shows three different methods for finding the GCF. Course 1

4 -3 Greatest Common Factor Additional Example 1 A: Finding the GCF Find the GCF of the set of numbers. 28 and 42 Method 1: List the factors of 28: 1, 2, 4, 7, 14, 28 List all the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Circle the GCF. The GCF of 28 and 42 is 14. Course 1

4 -3 Greatest Common Factor Additional Example 1 B: Finding the GCF Find the GCF of the set of numbers. 18, 30, and 24 Method 2: Use the prime factorization. 18 = 2 • 3 30 = 2 • 3 • 5 24 = 2 • 3 • 2 2 • 3= 6 Write the prime factorization of each number. Find the common prime factors. Find the product of the common prime factors. The GCF of 18, 30, and 24 is 6. Course 1

4 -3 Greatest Common Factor Additional Example 1 C: Finding the GCF Find the GCF of the set of numbers. 45, 18, and 27 Method 3: Use a ladder diagram. 3 45 18 27 3 15 6 9 5 2 3 • 3= 9 3 Begin with a factor that divides into each number. Keep dividing until the three have no common factors. Find the product of the numbers you divided by. The GCF of 45, 18, and 27 is 9. Course 1

4 -3 Greatest Common Factor Check It Out: Example 1 A Find the GCF of the set of numbers. 18 and 36 Method 1: List the factors of 18: 1, 2, 3, 6, 9, 18 List all the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Circle the GCF. The GCF of 18 and 36 is 18. Course 1

4 -3 Greatest Common Factor Check It Out: Example 1 B Find the GCF of the set of numbers. 10, 20, and 30 Method 2: Use the prime factorization. 10 = 2 • 5 20 = 2 • 5 • 2 30 = 2 • 5 • 3 2 • 5 = 10 Write the prime factorization of each number. Find the common prime factors. Find the product of the common prime factors. The GCF of 10, 20, and 30 is 10. Course 1

4 -3 Greatest Common Factor Check It Out: Example 1 C 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 40 16 24 each number. Keep dividing until the 2 20 8 12 three have no common factors. 2 10 4 6 5 2 3 2 • 2 =8 Find the product of the numbers you divided by. The GCF of 40, 16, and 24 is 8. Course 1

4 -3 Greatest Common Factor Additional Example 2: Problem Solving Application Jenna has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make? Course 1

4 -3 Greatest Common Factor 1 Understand the Problem The answer will be the greatest number of bouquets 16 red flowers and 24 yellow flowers can form so that each bouquet has the same number of red flowers, and each bouquet has the same number of yellow flowers. 2 Make a Plan You can make an organized list of the possible bouquets. Course 1

4 -3 Greatest Common Factor 3 Solve Red Yellow 2 3 Bouquets RR RR YYY YYY 16 red, 24 yellow: Every flower is in a bouquet The greatest number of bouquets Jenna can make is 8. 4 Look Back To form the largest number of bouquets, find the GCF of 16 and 24. factors of 16: 1, 2, 4, 8, 16 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The GCF of 16 and 24 is 8. Course 1

4 -3 Greatest Common Factor Check It Out: Example 2 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? Course 1

4 -3 Greatest Common Factor Check It Out: Example 2 Continued 1 Understand the Problem 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. 2 Make a Plan You can make an organized list of the possible fruit baskets. Course 1

4 -3 Greatest Common Factor 3 Solve Oranges Pears 2 3 Bouquets OO OO OO PPP PPP PPP 18 oranges, 27 pears: Every fruit is in a basket The greatest number of baskets Peter can make is 9. 4 Look Back To form the largest number of bouquets, find the GCF of 18 and 27. factors of 18: 1, 2, 3, 6, 9, 18 factors of 27: 1, 3, 9, 27 The GCF of 18 and 27 is 9. Course 1

4 -3 Greatest Insert Lesson Common Title. Factor Here Lesson Quiz: Part I Find the greatest common factor of each set of numbers. 1. 18 and 30 6 2. 20 and 35 5 3. 8, 28, 52 4 4. 44, 66, 88 22 Course 1

4 -3 Greatest Insert Lesson Common Title. Factor Here 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 Course 1