1. Tests are graded… Check Aeries! New Homework Stamp Logs Tomorrow 

2. Warmups
Multiply:
Solve the system: 3. 1.
Subtract: 2.

3. 10-1 Factors and Greatest Common Factors
Objective: To find prime factorizations and greatest common factors for monomials.
Standard 11.0

4. Factors
Factor: a number or variable that divides evenly into your original number.
Example 1: Find the factors of 72.
This problem is like #19-23 in homework tonight!

5. Some terms to know Prime: Only factors are 1 & itself
Composite: Having more than 2 factors
Write the prime numbers up to 20:
1, 2, 3, 5, 7, 11, 13, 17, 19

6. FACTOR TREE (for composite #s)
384
2 24
2 6
2 3
2•2•2•2•2•2•2•3
Prime factorization

7. TOO
1) 20 2) 36 2•2•5 2•2•3•3 Hints If it is an even, it is divisible by 2 If you add the digits and the answer is divisible by 3, then the original number is divisible by 3 If it ends in 0 or 5, it is divisible by 5 Stop trying when the answer is smaller than the number you divided by

8. Factoring with Variables
81b2c3
9 9
3•3•3•3•b•b•c•c•c
TOO
32abc3
2•2•2•2•2•a•b•c•c•c

9. Greatest Common Factor (GCF)
Make a factor tree and multiply together what they have in common
80 28
2 10
2 5
2•2 = 4 =GCF

10. GCF: Biggest number that will divide evenly into all of the numbers
With variables, take the smallest exponent
32xy2z, 48x3y4
2•2•2•2•2, 2•2•2•2•3
GCF: 16xy2
TOO for Homework
18xp2, 48x4

11. Challenge Problem – find the GCF

12. Homework
Greatest Common Factor Worksheet

13. Math Lab Warmups
Multiply: 3. 1.
Subtract: 2.

14. Example 1: Using a Factor Tree to Find Prime Factorization
Course 2
10-1
Prime Factorization
Example 1: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number.
A. 24
Write 24 as the product of
two factors. 24
8 · 3
Continue factoring until all
factors are prime.
4 · 2 · 3
2 · 2 · 2 · 3
The prime factorization of 24 is 2 · 2 · 2 · 3. Using
exponents, you can write this as 23 · 3.

15. Example 2: Using a Factor Tree to Find Prime Factorization
Course 2
10-1
Prime Factorization
Example 2: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number.
B. 150
150
Write 150 as the product
of two factors.
30 · 5
Continue factoring until
all factors are prime.
10 · 3 · 5
2 · 5 · 3 · 5
The prime factorization of 150 is 2 · 3 · 5 · 5, or
2 · 3 · 52.

16. Insert Lesson Title Here
Course 2
2-4
Prime Factorization
Insert Lesson Title Here
Try This: Example 3
Write the prime factorization of the number.
A. 36
Write 36 as the product of
two factors. 36
18 · 2
Continue factoring until all
factors are prime.
9 · 2 · 2
3 · 3 · 2 · 2
The prime factorization of 36 is 2 · 2 · 3 · 3. Using
exponents, you can write this as 22 · 32.

17. Insert Lesson Title Here
Course 2
10-1
Prime Factorization
Insert Lesson Title Here
Try This: Example 4
Write the prime factorization of the number.
B. 90 90
Write 90 as the product
of two factors.
45 · 2
Continue factoring until
all factors are prime.
9 · 5 · 2
3 · 3 · 5 · 2
The prime factorization of 90 is 3 · 3 · 5 · 2, or
2 · 32 · 5.

18. Your turn!  Prime Factorization Worksheet
Use scratch paper to make your factor trees.
Remember to list your factors in order from least to greatest.
Work Individually
Switch and grade when everyone is done 