Warm-upWarm-upList the factors for the following numbers:

1. 30

2. 66

3. 71

1, 2, 3, 5, 6, 10, 15, 30

1, 2, 3, 6,11, 22, 33, 66

1, 71

TestsTests(Pre Progress Reports)(Pre Progress Reports)

TextbooksTextbooks

My WebsiteMy Website

What am I Learning Today?What am I Learning Today?

Factors

Prime Factorization

How will I show that I learned it?How will I show that I learned it?Apply factors

Decompose Numbers into their Prime Factorization

VocabularyVocabularyPrime 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.

You can use factors to write a number in different ways.

Factorization of 12

2 • 61 • 12 3 • 4 3 • 2 • 2

The prime factorization of a

number is the number written as the product

of its prime factors.

Notice that these factors are all prime.

What do you notice about how the last set of factors are written?

A number is in exponential form when it is written with a base and an exponent.

7733Base

Exponent

= 7 7 7= 343

An exponent tells how many times a number called the base is used as a factor.

What is an exponent?What is an exponent?

To decompose a number into its prime

factorization, you may use the tree or the

ladder method.

Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor.

24

2 12•

6

2

2 •

3•

24

6 4•

3 2 2 2

24 = 2 • 2 • 2 • 3

24 = 3 • 2 • 2 • 2

The prime factorization of 24 is 2 • 2 • 2 • 3

• •

Write the prime factorization of 24Write the prime factorization of 24(using a factor tree)(using a factor tree)

The prime factorization of 24 is 2 • 2 • 2 • 3

To write your answer using To write your answer using exponentsexponents

2 • 3 3

Choose a prime factor of 24 to begin. Keep dividing by prime factors until the quotient is 1.

2 24

2

1

12

6

24 = 2 • 2 • 2 • 3

3 24

2

1

8

2 4

24 = 3 • 2 • 2 • 2

The prime factorization of 24 is 2 • 2 • 2 • 3

Write the prime factorization of 24Write the prime factorization of 24

(using a ladder)(using a ladder)

2

33 2 2

The prime factorization of 24 is 2 • 2 • 2 • 3

To write your answer using To write your answer using exponentsexponents

2 • 3 3

PracticePractice

45 Tree Method Ladder Method

PracticePractice

120 Tree Method Ladder Method

PracticePractice

72 Tree Method Ladder Method

PracticePractice

48 Tree Method Ladder Method

GroupsGroups

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