9.1 Factors and Greatest Common Factors

Part 2Objective:

To be able to find the greatest common factor of monomials.

GCFThe greatest common factor is the greatest

number that is a factor of both original numbers.

Hint:• The GCF of two or more monomials is the

product of the prime factors common to the integers.

Relatively PrimeIf two or more monomials have a GCF of 1, then

they are said to be relatively prime.

Give an example of two integers that are relatively prime.

Steps:• List the prime factorization of each term

horizontally.**Use the FACTOR TREE**

• Circle each number or variable that all of the terms have in common.

• Copy down each number or variable ONCE.• Multiply what you have. That is the GCF.

How to Use Prime Factorization to find the GCF of Two Monomials:

Example 1Find the GCF of each monomial using prime

factorization.a. 24 and 36

Example 1Find the GCF of each monomial using prime

factorization.b. 54, 63, and 180

Example 2Find the GCF of each monomial using prime

factorization.a. 36x2y and 54xy2z

Example 2Find the GCF of each monomial using prime

factorization.b. 12a2b and 90a2b2c

Example 2Find the GCF of each monomial using prime

factorization.c. 24gh and 36g2h2

Classwork

TB p. 478 #48 – 60 even

Homework

TB p. 478 #49 – 61 odd