Lesson 9-1 Factors and Greatest Common Factors

Definitions Prime Number - A whole number, greater than 1, whose only factors are 1 and itself. Composite Number - a whole number, greater than 1, that has more than two factors. 17 = 1  = 2  6 12 = 3  4 12 = 1  12

Factor each number. Then classify each number as prime or composite.

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 = 2  3  3  5 Use a factor tree  10 3  3  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. 12a 2 b 3 = 2  6  a  a  b  b  b = 2  2  3  a  a  b  b  b -66pq 2 = -1  66  p  q  q = -1  6  11  p  q  q = -1  2  3  11  p  q  q

Factor each monomial completely. 18x 3 y 3 -26rst 2

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 - 36x 2 y = 2  2  3  3  x  x  y 54xy 2 z = 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 27a 2 b and 15ab 2 c