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Do Now 2/8/11 Take out HW from Friday. Text page 179, #12-27 all, & 32 Copy HW in your planner. Text page 179, #28-31 all, 33, 37-45 all Quiz sections 4.1 & 4.2 Wednesday. In your journal, explain why a single number does not have a GCF. Then find the GCF of 96 and 54. Homework Text page 179, #12-27 all, & 32 12) 14 13) 3 14) 17 15) 12 16) 1 17) 1 18) 2 19) 120 20) 1; relatively prime 21) 11; not relatively prime 22) 3; not relatively prime 23) 1; relatively prime 24) 2; not relatively prime 25) 1; relatively prime 26) 16; not relatively prime 27) 28; not relatively prime 32) 8 bands; 4 vocalists Objective SWBAT find the greatest common factor of two or more whole numbers SWBAT find the greatest common factor of two or more monomials Section 4.2 “Greatest Common Factor” Greatest Common Factor The LARGEST common factor of two numbers. Find the GCF of 8 and 12. List the factors of the two numbers and then compare. 8: 1, 2, 4, 8 12: 1, 2, 3, 4, 6, 12 From the list you can see that 1, 2, and 4 are common factors. Of these 4 is the greatest common factor. Greatest Common Factors Find the GCF of 180 and 378. When the numbers are too large to list the factors of the two numbers, find the prime factorization of each and then compare. 180: 2 · 2 · 3 · 3 · 5 378: 2 · 3 · 3 · 3 · 7 From the list you can see that 2, 3, and 3 are common prime factors. The greatest common factor of 180 and 378 is the product of 2 · 3 · 3 which is 18. Greatest Common Factors Find the GCF of 39 and 50. When the numbers are too large to list the factors of the two numbers, find the prime factorization of each and then compare. 39: 3 · 13 50: 2 · 5 · 5 Relatively Prime: Two numbers are relatively prime if their greatest common factor is 1. From the list you can see that there are NO common prime factors. However, two numbers always have 1 as a common factor. So the GCF is 1 and the two numbers are relatively prime. GCF of Variable Expressions Find the GCF of 12x²y and 6xy³. Write the prime factorization of each and then compare. 12x²y: 2·2·3·x·x·y 6xy³: 2·3·x·y·y·y From the list you can see that 2, 3, x, and y are common prime factors. The greatest common factor is the product of 2 · 3 · x · y, which is 6xy. GCF of Variable Expressions Find the GCF of 18xy² and 28x²y³. Write the prime factorization of each and then compare. 18xy²: 2·3·3·x·y·y 28x²y³: 2·2·7·x·x·y·y·y From the list you can see that 2, x, y, and y are common prime factors. The greatest common factor is the product of 2 · x · y · y, which is 2xy². Greatest Common Factors Find the GCF of 12x²y, 18xy³, and 30x²y³. List the factors of the three numbers and then compare. 12x²y: 2·2·3·x·x·y 18xy³: 2·3·3·x·y·y·y 30x²y³: 2 · 3 · 5 · x · x · y · y · y From the list you can see that 2, 3, x, and y are common prime factors. The greatest common factor is the product of 2 · 3 · x · y, which is 6xy. Greatest Common Factors Find the GCF of 48a²b, 64ab³, and 80a²b³. 48a²b : 2·2·2·2·3·a·a·b 64ab³ : 2·2·2·2·2·2·a·b·b·b 80a²b³ : 2 · 2 · 2 · 2 · 5 · a · a · b · b · b From the list you can see that 2, 2, 2, 2, a, and b are common prime factors. The greatest common factor is the product of 2 · 2 · 2 · 2 · a · b which is 16ab. 24 Homework Text page 179, #28-31 all, 33, 37-45 all