Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Greatest Common Factor for Visual Learners Fortner Common Core Standard Compute fluently with multi-digit numbers and find common factors and multiples. CC.6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. use the distributive property to express a sum of two whole numbers with no common factor. Lesson Objective Find the greatest common factor of two whole numbers. ESSENTIAL QUESTION: How can you find the greatest common factor of two whole numbers? VOCABULARY: COMMON FACTOR: a number that is a factor of two or more numbers. GREATEST COMMON FACTOR: (GCF) the greatest factor that two or more numbers have in common. Problem of the Day TEST PREP: A group of students are helping pass out fliers for a bake sale. They have 1,500 fliers to pass out. If they want to pass out all of the fliers in 3 hours, how many fliers do they need to pass out each hour? A 5, 000 C 50 B 500 D 5 Greatest Common Factor A common factor is a number that is a factor of two or more numbers. The numbers 16 and 20 have 1, 2, and 4 as common factors. FACTORS OF 16 : 1, 2, 4, FACTORS OF 20: 1, 2, 4, 5, 8, 16 10, 20 The GREATEST COMMON FACTOR (GCF) is the greatest factor that two Or more numbers have in common. The GREATEST COMMON FACTOR or GCF of 16 and 20 is 4. REMEMBER A number that is multiplied by another number to find a product is a factor. Factors of 6: 1, 2, 3, 6 Factors of 9: 1, 3, 9 Every number has 1 as a factor. Unlock the Problem Jim is cutting two strips of wood to make picture frames. The wood strips measure 12 inches and 18 inches. He wants To cut the strips into equal lengths that are as long as possible. Into what lengths should he cut the wood? Find the greatest common factor, or GCF of 12 and 18. One Way: Use a list FACTORS OF 12 : 1, 2, ___, 3 ___, 4 ___, 6 12 FACTORS OF 18: 1, ___, 2 ___, 3 ___, 6 ___, 9 ___ 18 The GREATEST COMMON FACTOR, or (GCF), is ____ 6 MATH TALK Into what other lengths could Jim cut the wood to obtain equal lengths? 1- inch, 2- inch, or 3-inch lengths Another Way: Use Prime Factorization. Write the prime factorization of each number. 12 = 2 x ____ 2 x3 2 x 3 x ____ 3 18 = ____ Place the prime factors of the Numbers in the appropriate parts Of the Venn Diagram Prime factors of 12 2 2 3 Prime factors of 18 3 Common Prime Factors To find the GCF, find the product of the common prime factors. 2 x 3 = 6 The GCF is 6 So, Jim should cut the wood into _____ 6 -inch lengths. Distributive Property Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. 5 x (8 + 6) = (5 x 8) + (5 x 6) You can use the Distributive Property to express the sum of two whole numbers as a product if the numbers have a common factor. Example: Use the GCF and the Distributive Property to express 36 + 27 as a product. Find the GCF of 36 and 27 Write each number as the product of the GCF and another factor. 9 GCF: ______ 36 + 27 3 4 + (9 x ____) (9 x ___) Use the Distributive Property to Write 36 + 27 as a product. Check your answer. 9 x (4 + ___) 3 63 36 + 27 = _____ 9 x (4 + ___) 3 = 9 x ___ 7 = ___ 63 9 x (___ 4 + ___). 3 So, 36 + 27 = ___ 1. Explain two ways to find the GCF of 36 and 27. List the factors of each number and circle the GCF. Another Way: Write the prime factorization of each number and find the product of the common prime factors. 2. Describe how the figure at the right shows that 36 + 27 = 9 x (4 + 3 ) The model shows an array with 36 + 27 = 63 squares. The array has 9 rows and is divided into two parts, one part with 4 columns 9 and one part with 3 columns. So, the model shows 9 rows of 4 columns plus 3 columns, or 9 x (4 + 3) squares 4 3 9x4 9x3 Share and Show 1. List the factors of 12 and 20. Circle the GCF FACTORS OF 12 : ___,___, 1 2 ___, 3 ___, 4 ___, 6 ___ 12 1 2 ___, 4 ___, 5 ___, 10 ___ 20 FACTORS OF 20: ___,___, Find the GCF. 2. 16, 18 3. 25, 40 2 5 4. 24, 40 5. 14, 35 8 7 Use the GCF and the Distributive Property to express the sum as a product. 6. 21 + 28 7. 15 + 27 7 x (3 + 4) 3 x (5 + 9) MATH TALK 8. 40 + 15 9. 32 + 20 5 x (8 + 3) 4 x (8 + 5) Explain how to use the prime factorization of two numbers to find their GCF. Write the prime factorization of each number. Then find the prime factors that are common to the two numbers. The GCF is the product of the common prime factors. On Your Own Find the GCF. 10. 8, 12 4 11. 27, 45 9 12. 30, 45 13. 42, 63 15 21 14. 8, 25 15. 31, 32 16. 56, 64 17. 150, 275 1 1 8 25 Use the GCF and the Distributive Property to express the sum as a product. 18. 24 + 30 19. 49 + 14 20. 40 + 15 21. 60 + 12 6 x (4 + 5) 7 x (7 + 2) 9 x (7 + 9) 12 x (5 + 1) Problem Solving Use the table for 22 – 25. Teachers at the Scott School of Strings Teach only one instrument in each class. Scott School of Strings Instrument Number of students Bass 20 Cello 27 Viola 30 Violin 36 Scott School of Strings Instrument Number of students Bass 20 Cello 27 Viola 30 Violin 36 22. Francisco teaches group lessons to all of the violin and viola Students at the Scott School of Strings. All of his classes have the same number of students. What is the greatest number of students he can have in class? 6 Scott School of Strings Instrument Number of students Bass 20 Cello 27 Viola 30 Violin 36 23. Amanda teaches music history lessons to all of the cello, viola, and violin students. All her classes have the same number of students. What is the greatest number of students she can have in each class? 3 Scott School of Strings Instrument Number of students Bass 20 Cello 27 Viola 30 Violin 36 24. Mila teaches jazz classes. She has 9 students in each class, and she teaches a all the students who play two instruments. How many students does she have, and which two instruments does she teach? 63; cello and violin Scott School of Strings Instrument Number of students Bass 20 Cello 27 Viola 30 Violin 36 25. WRITE MATH: Explain how you could use the GCF and the Distributive Property to express the sum of the number of bass students and the number of violin students as a product. Find the GCF of 20 and 36: 4 Then write 20 and 30 as a product of 4 and another factor. Finally, use the Distributive Property to write 20 + 36 as a product: 4 x (5 + 9) Test Prep 26. Tina has 3 ribbons measuring 18 inches, 24 inches, and 36 inches. She wants to cut them into equal pieces that are as long as possible. Into what lengths should she cut the ribbons? A 3 inches C 6 inches B 4 inches D 12 inches VOCABULARY: Common factor: a number that is a factor of two or more numbers. Greatest common factor (GCF): the greatest factor that two or more numbers have in common. Least common multiple (LCM): the least number that is a common Multiple of two or more numbers. Prime factorization: a number written as the product of all its prime factors. Compatible numbers: numbers that are easy to compute with mentally. VOCABULARY: Decimal: a number with one or more digits to the right of the decimal point. Dividend: the number that is to be divided in a division problem. Divisor: the number that divides the dividend. Prime numbers: a number that has exactly two factors, one and itself. Quotient: the number, not including the remainder, that results from dividing.