Module 2 lesson 19
- 4. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 4 January 09, 2015 Nov 172:28 PM When finding the GCF of two numbers, we looked at many strategies: 1 - Making a List: 2 - Using Prime Factorization: 3 - And today we will look at: Euclid's Algorithm method GCF of 30 & 50 = 2 x 5 = 10
- 5. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 5 January 09, 2015 Nov 172:29 PM Euclid’s Algorithm is used to find the greatest common factor (GCF) of two whole numbers. 1. Divide the larger of the two numbers by the smaller one. 2. If there is a remainder, divide it into the divisor. 3. Continue dividing the last divisor by the last remainder until the remainder is zero. 4. The final divisor is the GCF of the original pair of numbers. Euclid's Algorithm Let's look at an example on the next slide: Today’s lesson is inspired by Euclid, a Greek mathematician, who lived around 300 BCE. He discovered a way to find the greatest common factor of two numbers that is based on long division.
- 6. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 6 January 09, 2015 Nov 172:29 PM Let's skip to Example 2 so we can practice the steps: 1. Divide the larger of the two numbers by the smaller one. 2. If there is a remainder, divide it into the divisor. 3. Continue dividing the last divisor by the last remainder until the remainder is zero. 4. The final divisor is the GCF of the original pair of numbers. a. Let’s apply Euclid’s Algorithm to some of the problems from our last lesson. i. What is the GCF of 30 and 50? ii. Using Euclid’s Algorithm, we follow the steps that are listed in the opening exercise
- 8. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 8 January 09, 2015 Nov 172:29 PM Example 3: Larger Numbers GCF (96, 144) GCF (660, 840) tap here for answer tap here for answer
- 14. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 14 January 09, 2015 Nov 172:28 PM We already know the GCF of (30,50) is 10. Squares of 10 inches by 10 inches will tile the area. b. If we use squares that are 10 by 10, how many will we need? c. If this were a giant chunk of cheese in a factory, would it change the thinking or the calculations we just did? d. How many 10 inch ×10 inch squares of cheese could be cut from the giant 30 inch × 50 inch slab?
- 15. Module 2 Lesson 19 The Euclidean Algorithm as an Application of the Long Division Algorithm.noteb 15 January 09, 2015 Aug 268:21 PM Closing Please take out your exit ticket for Lesson 19, close your binder, and complete the exit ticket. This will be collected. Euclid’s Algorithm is used to find the greatest common factor (GCF) of two whole numbers. The steps are listed on your Student Page and need to be followed enough times to get a zero remainder. With practice, this can be a quick method for finding the GCF.