1. 4-2 Greatest Common Factor Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. 4-2 Greatest Common Factor Warm Up Write the prime factorization of each number. 1. 143. 63 2. 184. 54 2  73 2  7 2  3 2 2  3 3

3. 4-2 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

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

5. 4-2 Greatest Common Factor Vocabulary greatest common factor (GCF) ‏

6. 4-2 Greatest Common Factor 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: Common factors: 1,2,3,4,6, 8, 1, 2, 3, 4, 6, The greatest common factor (GCF) of 24 and 36 is 12. Example 1 shows three different methods for finding the GCF. 1,2,3,4,6, 9, 12, 12, 18, 24 36 12

7. 4-2 Greatest Common Factor Additional Example 1A: Finding the GCF Find the GCF of the set of numbers. 28 and 42 Method 1: List the factors. factors of 28: factors of 42: 1,2,14,7,28 7,1, 4, 3,2,426,21,14, List all the factors. Circle the GCF. The GCF of 28 and 42 is 14.

8. 4-2 Greatest Common Factor Additional Example 1B: Finding the GCF Find the GCF of the set of numbers. 18, 30, and 24 Method 2: Use the prime factorization. 18 = 30 = 24 = 2 5 3 2 2 3 2 3 2 3 Write the prime factorization of each number. Find the common prime factors. The GCF of 18, 30, and 24 is 6. Find the prime factors common to all the numbers. 2 3 =6

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

10. 4-2 Greatest Common Factor Check It Out: Example 1A Find the GCF of the set of numbers. 18 and 36 Method 1: List the factors. factors of 18: factors of 36: 1,2, 9,6,18 6,1, 3, 2,364,12,9, List all the factors. Circle the GCF. The GCF of 18 and 36 is 18. 18,

11. 4-2 Greatest Common Factor Check It Out: Example 1B Find the GCF of the set of numbers. 10, 20, and 30 Method 2: Use the prime factorization. 10 = 20 = 30 = 2 2 3 2 5 2 5 5 Write the prime factorization of each number. Find the common prime factors. The GCF of 10, 20, and 30 is 10. Find the prime factors common to all the numbers. 2 5 =10

12. 4-2 Greatest Common Factor Check It Out: Example 1C Find the GCF of the set of numbers. 40, 16, and 24 Method 3: Use a ladder diagram. 2 2 40 16 24 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. 2 2 2 =2 2 2 = The GCF of 40, 16, and 24 is 8. 8 20 8 12 5 2 3 10 4 62

13. 4-2 Greatest Common Factor Check For Understanding 1. 18 and 30 2. 20 and 35 3. 8, 28, 52 4. 44, 66, 88 5 6 4 22 Find the greatest common factor of each set of numbers.

14. 4-2 Greatest Common Factor Lesson Quiz for Student Response Systems 1. Identify the greatest common factor of 28 and 36. A. 2 B. 4 C. 6 D. 7

15. 4-2 Greatest Common Factor Lesson Quiz for Student Response Systems 2. Identify the greatest common factor of 49 and 77. A. 3 B. 5 C. 7 D. 11

16. 4-2 Greatest Common Factor 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

17. 4-2 Greatest Common Factor 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