1. ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

2. ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-1 Warm Up

3. ALGEBRA READINESS “Greatest Common Divisor” (4-2) What is a “common divisor”? What is the “greatest common divisor? Common Divisor: a divisor (factor) that two or more numbers share Example: What are the common divisors of 18 and 24? Divisors of 18: 1, 2, 3, 6, 9, 18 Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The common divisors of 18 and 24 are 1, 2, 3, and 6. Greatest Common Divisor (also known as the GCF): the largest common divisor shared by two or more numbers Example: What is the GCF of 20 and 42? Divisors of 20: 1, 2, 4, 5, 10, 20 Divisors of 12: 1, 2, 3, 4, 6, 12 The greatest common divisors or GCF of 20 and 12 is 4.

4. ALGEBRA READINESS List the divisors to find the GCD of 48 and 64. List the divisors of 48 and the divisors of 64. Then circle the common divisors. Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Divisors of 64: 1, 2, 4, 8, 16, 32, 64 The greatest common divisor (GCD) is 16. The common divisors are 1, 2, 4, 8, and 16. Greatest Common Divisor LESSON 4-2 Additional Examples

5. ALGEBRA READINESS “Greatest Common Divisor” (4-2) How can you use prime factorization to find the GCD? To use prime factorization to find the GCD: 1.Find the prime factorization of each number. 2.Multiply the common factors together. Example: Find the GCF of 18, 27, and 36. Factor Trees for 18, 27, and 36 1. Write the prime factorization for each number. 2. Multiply common factors. The GCD of 18, 27, and 36 is 9.

6. ALGEBRA READINESS Two ribbons have lengths of 28 cm and 42 cm. You cut both ribbons into pieces of equal length with nothing left over. What is the greatest possible length of the pieces? Make a factor tree to find the prime factorization of each number. 214 2727 28 7272 14 3 42 To find the greatest possible lengths of the pieces, find the GCD of 28 and 42. Greatest Common Divisor LESSON 4-2 Additional Examples

7. ALGEBRA READINESS The GCD of 28 and 42 is 14, so the greatest possible length of the pieces is 14 cm. 2  7 = 142. Multiply the common factors. Identify common factors. 1. Write the prime factorization for each number. 28 = 2 2 7 42 = 2 3 7     (Continued) Greatest Common Divisor LESSON 4-2 Additional Examples

8. ALGEBRA READINESS Find the GCD of each set of numbers. 1.60, 802.24, 57 3.36, 484.115, 70, 200 20 3 12 5 Greatest Common Divisor LESSON 4-2 Lesson Quiz