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Math 35 Fall Term Professor Carl Scarbnick scarbnick@gmail

Math 35 Fall Term Professor Carl Scarbnick scarbnick@gmail.com. Topic: Greatest Common Divisor. Section 1.6 Greatest Common Divisor. What is a greatest common divisor (GCD) Finding the greatest common divisor with prime factorization

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Math 35 Fall Term Professor Carl Scarbnick scarbnick@gmail

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  1. Math 35 Fall TermProfessor Carl Scarbnickscarbnick@gmail.com Topic: Greatest Common Divisor

  2. Section 1.6 Greatest Common Divisor What is a greatest common divisor (GCD) Finding the greatest common divisor with prime factorization The graphics in these slides depend on the screen resolution of your monitor. Please use the handout passed out on Aug 28, 2007 if you experience any problems. These slides are intended to supplement the reading in the Textbook. They are not a substitute for the material in the textbook. Add additional notes as we discuss these slides in class Objectives

  3. 1.6 Greatest Common Divisor Objective 1. What is a greatest common divisor (GCD) The greatest common divisor (GCD) of two natural numbers is the largest divisor shared by these two numbers.

  4. 1.6 Greatest Common Divisor Objective 1. What is a greatest common divisor (GCD) Example: Find the GCD of 12 and 16 Divisors of 12: 1, 2, 3, 4, 6, 12 Multiples of 16: 1, 2, 4, 8, 16 The largest number found in each list is 4. This means that 4 is the greatest common divisor (GCD) of 12 and 16.

  5. 1.6 Greatest Common Divisor Objective 2. Find the GCD using prime factorization. Example: Find the GCD of 12 and 16 The prime factorization of 12 = 2 x 2 x 3 The prime factorization of 16 = 2 x 2 x 2 x 2 Notice that 2 x 2 appears in each prime factorization. This means 2 x 2 = 4 is a divisor of 12 and a divisor of 16. The GCD of 12 and 16 is 4.

  6. 1.6 Greatest Common Divisor Objective 2. Find the GCD using prime factorization. General Procedure for computing the GCD with prime factorization: Step 1: Write the prime factorization of each number. I recommend using factor trees. Step 2: Take the product of the prime numbers that are common to both lists. If a prime number appears more than one time in a list, use it the least number of times it appears in a list.

  7. 1.6 Greatest Common Divisor Objective 2. Find the GCD using prime factorization. Problem 1: Find the greatest common divisor of 42 and 70 Step 1: The prime factorization of 42 is 42 = 2 x 3 x 7 The prime factorization of 70 is 70 = 2 x 5 x 7 Step 2 GCD = 2 x 7 = 14

  8. 1.6 Greatest Common Divisor Objective 2. Find the GCD using prime factorization. Problem 2: Find the greatest common divisor of 60 and 72. Step 1: The prime factorization of 60 is 60 = 2 x 2 x 3 x 5 The prime factorization of 72 is 72= 2 x 2 x 2 x 3 x 3 Step 2 GCD = 2 x 2 x 3 = 12

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