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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
=2335
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
•
=223aabbb
•-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