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Lesson 9-1 Factors and Greatest Common Factors Definitions •Prime Number - A whole number, greater than 1, whose only factors are 1 and itself. 17 = 1 17 •Composite Number - a whole number, greater than 1, that has more than two factors. 12 = 2 6 12 = 3 4 12 = 1 12 Factor each number. Then classify each number as prime or composite. a. 22 b. 31 Definitions •Prime Factorization - When a whole number is expressed as the product of factors that are all prime numbers. •Ex. 90 = 2 45 = 2 3 15 Use a factor tree. 90 =2335 9 3 3 10 2 5 •Prime Factorization of a Negative Number - The first prime factor is -1. Find the prime factorization of 84. Find the prime factorization of -132. Definitions •Factored Form - A monomial is in factored form when it is expressed as the product of prime numbers and variables and no variable has an exponent greater than 1. •12a2b3 = 2 6 a a b b b • =223aabbb •-66pq2 = -1 66 p q q • = -1 6 11 p q q • = -1 2 3 11 p q q Factor each monomial completely. 18x3y3 -26rst2 Definitions •Greatest Common Factor (GCF) - The greatest number that is a factor of both original numbers. •48 = 2 2 2 2 3 •60 = 2 2 3 5 GCF = 2 2 3 = 12 •GCF of a Set of Monomials •36x2y = 2 2 3 3 x x y •54xy2z = 2 3 3 3 x y y z GCF = 2 3 3 x y = 18xy Find the GCF of each set of monomials. 12 and 18 27a2b and 15ab2c