1. List the factors for the following numbers:
Warm-up
List the factors for the following numbers: 30 66 71
1, 2, 3, 5, 6, 10, 15, 30
1, 2, 3, 6,11, 22, 33, 66
1, 71

2. Tests (Pre Progress Reports) Textbooks My Website

3. What am I Learning Today?
Factors
Prime Factorization
How will I show that I learned it?
Apply factors
Decompose Numbers into their Prime Factorization

4. Vocabulary
Prime Factorization: A number written as the product of its prime factors.
Exponent: Tells how many times a number (the base) is used as a factor.

5. What do you notice about how the last set of factors are written?
You can use factors to write a number in different ways.
Factorization of 12
Notice that these factors are all prime.
3 • 4
3 • 2 • 2
1 • 12
2 • 6
What do you notice about how the last set of factors are written?
The prime factorization of a number is the number written as the product of its prime factors.

6. 73 What is an exponent? = 7  7  7= 343
An exponent tells how many times a number called the base is used as a factor.
A number is in exponential form when it is written with a base and an exponent.
Exponent 73
Base
= 7  7  7= 343

7. To decompose a number into its prime factorization, you may use the tree or the ladder method.

8. Write the prime factorization of 24
(using a factor tree)
Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor. 24 24 2 • 12 6 • 4 2 • 6 3 • 2 2 • 2 2 • 3
24 = 3 • 2 • 2 • 2
24 = 2 • 2 • 2 • 3
The prime factorization of 24 is 2 • 2 • 2 • 3

9. To write your answer using exponents
The prime factorization of 24 is 2 • 2 • 2 • 3 3
2 • 3

10. Write the prime factorization of 24
(using a ladder)
Choose a prime factor of 24 to begin. Keep dividing by prime factors until the quotient is 1. 2 24 3 24 2 12 2 8 2 6 2 4 3 3 2 2 1 1
24 = 2 • 2 • 2 • 3
24 = 3 • 2 • 2 • 2
The prime factorization of 24 is 2 • 2 • 2 • 3

11. To write your answer using exponents
The prime factorization of 24 is 2 • 2 • 2 • 3 3
2 • 3

12. Tree Method Ladder Method
Practice 45
Tree Method Ladder Method

13. Tree Method Ladder Method
Practice
120
Tree Method Ladder Method

14. Tree Method Ladder Method
Practice 72
Tree Method Ladder Method

15. Tree Method Ladder Method
Practice 48
Tree Method Ladder Method

16. Groups Go to the color of your group.
Each person must be able to factor all problems in your clip to prime factors using both the ladder method and the tree method.
When time is called, a member of your group will be called to the front to factor one of your problems to primes using one of the methods.
You don’t know which member
You don’t know which problem
You don’t know which method