Transcript prime factorization

Warm-up
List the factors for the following numbers:
1. 30
1, 2, 3, 5, 6, 10, 15, 30
2. 66
1, 2, 3, 6,11, 22, 33, 66
3. 71
1, 71
Tests
(Pre Progress Reports)
Textbooks
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What am I Learning Today?
Factors
Prime Factorization
How will I show that I learned it?
Apply factors
Decompose Numbers into their Prime
Factorization
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.
You can use factors to write a number
in different ways.
Factorization of 12
1 • 12
2•6
3•4
3•2•2
Notice that
these factors
are all prime.
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.
What is an exponent?
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
Base
3
=
7

7

7=
343
7
To decompose a number into its prime
factorization, you may use the tree or the
ladder method.
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
2
•
24
2
•
6
12
•
6
2
•
3
3
•
2
4
2
•
2
24 = 3 • 2 • 2 • 2
24 = 2 • 2 • 2 • 3
The prime factorization of 24 is 2 • 2 • 2 • 3
To write your answer using
exponents
The prime factorization of 24 is 2 • 2 • 2 • 3
3
2 • 3
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
2
3
24
12
2 8
2 6
2
3
3
1
24 = 2 • 2 • 2 • 3
4
2 2
1
24 = 3 • 2 • 2 • 2
The prime factorization of 24 is 2 • 2 • 2 • 3
To write your answer using
exponents
The prime factorization of 24 is 2 • 2 • 2 • 3
3
2 • 3
Practice
Tree Method
45
Ladder Method
Practice
Tree Method
120
Ladder Method
Practice
Tree Method
72
Ladder Method
Practice
Tree Method
48
Ladder Method
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