1. Ch 4.4 – Greatest Common Factor
MJ2A
Ch 4.4 – Greatest Common Factor

2. Bellwork
Factor each monomial
77x
-23n3
30cd2

3. Assignment Review
Text p. 162 # 25 – 40

4. 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!

5. Objective – Ch 4.4
Students will find the greatest common factor of two or more numbers or monomials

6. 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, 12
Factors 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

7. 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 factors
Do a factor tree for each number of monomial
Use 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…

8. Example Find the GCF of 30 & 24: 2 30 , 24 3 15 , 6 5 , 2
2 30 , 24
3 15 , 6
5 , 2
GCF = 2 x 3 = 6

9. Example Find the GCF of 54, 36, & 45 3 54, 36, 45 3 18, 12, 15 6, 4, 5
3 54, 36, 45
3 18, 12, 15
6, 4, 5
GCF = 3 x 3 = 9

10. Your Turn
In the notes section of your notebook write the numbers and then find the GCF using the cake method
28, 35
12, 48, 72
Ans: 1 = 7; 2 = 12

11. Factoring Monomials You can use the same method to factor monomials…
Let’s look at an example…

12. Example Find the GCF of 30a3b2, 24a2b 3ab 30a3b2, 24a2b 2a 10a2b 8a
Prime Factorization = 3ab ∙ 2a = 6a2b

13. Your Turn
In the notes section of your notebook write and do the prime factorization of the following monomials:
12x, 40x2
4st, 10s

14. 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 ∙ x
6 = 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)

15. Your Turn
In the notes section of your notebook write the expression and then factor using the distributive property
3n + 9
t2 + 4t x

16. 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

17. Assignment Text p. 167 # 25 – 30 & 44 – 52 Reminder
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!