MJ2A

Ch 4.4 – Greatest Common Factor

Bellwork

• Factor each monomial

1. 77x

2. -23n3

3. 30cd2

Assignment Review

• Text p. 162 # 25 – 40

Before we begin…

• Please take out your notebook and get ready to work…

• Yesterday we looked at factoring numbers…we will use what we learned to determine the Greatest Common Factor (GCF) of 2 or more numbers…

• This is real easy…so pay attention!

Objective – Ch 4.4

• Students will find the greatest common factor of two or more numbers or monomials

Greatest Common Factor• The greatest common factor of two or more

numbers is as the name suggest the largest number that both numbers have in common..

• Example: To find the GCF of 12 & 20, you can list the factors:

Factors of 12: 1, 2, 3, 4, 6, 12Factors of 20: 1, 2, 4, 5, 10, 20

As you can clearly see…both numbers have common factors of 1, 2 and 4.

Of the common factors 4 is the largest. Therefore, the GCF of 12 & 20 is 4

Greatest Common Factor

• Like factoring numbers and monomial there are a number of ways to determine the greatest common factor of two or more numbers…

• You can List the factorsDo a factor tree for each number of monomialUse the cake method for each…

• For today’s lesson I will focus on the cake method because it is extremely easy to do…

• Let’s look at an example…

Example

Find the GCF of 30 & 24:

2 30 , 24

3 15 , 6

5 , 2

GCF = 2 x 3 = 6

Example

Find the GCF of 54, 36, & 45

3 54, 36, 45

3 18, 12, 15

6, 4, 5

GCF = 3 x 3 = 9

Your Turn

• In the notes section of your notebook write the numbers and then find the GCF using the cake method

1. 28, 35

2. 12, 48, 72

Factoring Monomials

• You can use the same method to factor monomials…

• Let’s look at an example…

Example

Find the GCF of 30a3b2, 24a2b

3ab 30a3b2, 24a2b

2a 10a2b8a

5ab 4

Prime Factorization = 3ab ∙ 2a = 6a2b

Your Turn

• In the notes section of your notebook write and do the prime factorization of the following monomials:

1. 12x, 40x2

2. 4st, 10s

Factoring Expressions

• You can use the distributive property to factor expressions

Example Factor 2x + 6• First find the GCF of 2x and 6

2x = 2 ∙ x6 = 2 ∙ 3

• Then write each term as a product of the GCF and its remaining factors

2x + 6 = 2(x) + 2(3) = 2(x + 3)

Your Turn

• In the notes section of your notebook write the expression and then factor using the distributive property

1. 3n + 9

2. t2 + 4t

3. 15 + 20x

Summary

• In the notes section of your notebook summarize the key concepts covered in today’s lesson

• Today we discussed:• Factoring using the cake method• Factoring monomials• Factoring expressions

Assignment

• Text p. 167 # 25 – 30 & 44 – 52Reminder

• I do not accept late assignments• You must show your work…(no work = no

credit)• Check your answers to the odd problems in the

back of the book…• If you did not get the same answer…you need

to problem solve to find out what you did wrong!