7th Grade Accelerated – Chapter 6 Supplementary Lesson 2
Greatest Common Factor of Monomials
Goal: Find the GCF of monomials.
Guiding Questions: How can you use the prime factors of algebraic expressions to find the GCF?
Warm-up:
Algebraic expressions involve numbers and variables. When you are finding the factors of the expression,
you must find the factors of both parts.
For example: Find the factors of
Prime factors of 75 are
Prime factors of x² are
So the factors of 75x² are
3·5·5
x·x
3·5·5 ·x·x
Find all of the factors of the following expressions:
1)
2)
3)
4) What factors do the answers to numbers 1 and 2 have in common?
5) What factors do the answers to numbers 2 and 3 have in common?
6) What factors do the answers to numbers 1 and 3 have in common?
Vocabulary:
monomial:
d)
1
b)
c)
Page
Example 1 – Factors of a Monomial
Question 1: What are the factors of a monomial?
Find the factors of the following monomials:
a)
Now You Try It! Find the factors of the monomial.
a)
c)
b)
d)
Example 2 – Greatest Common Factor of Multiple Monomials
Question 2: How can you use the prime factors of algebraic expressions to find the GCF?
Find the GCF of the monomials:
a) 36 and 45
c)
d)
and
and
and
2
e)
and
Page
b)
and
Now You Try It! Find the GCF of the monomials.
a) 24 and 18
c)
d)
and
and
and 8
3
e)
and
Page
b)
and