4 2 Greatest Common Factor I CAN find

  • Slides: 15
Download presentation
4 -2 Greatest Common Factor I CAN find the greatest common factor (GCF) of

4 -2 Greatest Common Factor I CAN find the greatest common factor (GCF) of a set of numbers.

4 -2 Greatest Common Factor Vocabulary greatest common factor (GCF)

4 -2 Greatest Common Factor Vocabulary greatest common factor (GCF)

4 -2 Greatest Common Factors shared by two or more whole numbers are called

4 -2 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: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 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.

4 -2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of

4 -2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of the set of numbers. A. 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.

4 -2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of

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

4 -2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of

4 -2 Greatest Common Factor Example 1: Finding the GCF Find the GCF of the set of numbers. C. 45, 18, and 27 Method 3: Use a ladder diagram. 3 45 18 27 3 15 6 9 5 2 3 3 • 3= 9 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.

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the set of numbers. A. 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.

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the set of numbers. B. 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 prime factors common to all the numbers. The GCF of 10, 20, and 30 is 10.

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the

4 -2 Greatest Common Factor You Try! Example 1 Find the GCF of the set of numbers. C. 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.

4 -2 Greatest Common Factor Example 2: Problem Solving Application Jenna has 16 red

4 -2 Greatest Common Factor 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? The greatest number of bouquets Jenna can make is 8.

4 -2 Greatest Common Factor You Try! Example 2 Peter has 18 oranges and

4 -2 Greatest Common Factor You Try! 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? The greatest number of baskets Peter can make is 9.

4 -2 Greatest Common Factor Reflection CAN YOU find the GCF of a set

4 -2 Greatest Common Factor Reflection CAN YOU find the GCF of a set of numbers?

4 -2 Greatest Common Factor Lesson Quiz: Part I Find the greatest common factor

4 -2 Greatest Common Factor 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

4 -2 Greatest Common Factor Lesson Quiz: Part II Find the greatest common factor

4 -2 Greatest Common Factor 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

4 -2 Greatest Common Factor HOMEWORK

4 -2 Greatest Common Factor HOMEWORK