Transcript 4-1

4-1 Factors and Prime Factorization
Do Now
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-1 Factors and Prime Factorization
Do Now – In your notebook
Identify each number as prime or
composite.
1. 19
prime
2. 82
composite
3. 57
composite
4. 85
composite
5. 101 prime
6. 121 composite
4-1 Factors and Prime Factorization
Objective:
• SWABAT write prime factorizations of
composite numbers.
4-1 Factors and Prime Factorization
Vocabulary
Factor
prime factorization
Greatest common factor (GCF)
4-1 Factors and Prime Factorization
Whole numbers that are multiplied to
find a product are called factors of that
product. A number is divisible by its
factors.
2 3=6
Factors
Product
6 ÷3 = 2
6 ÷2 = 3
6 is divisible
by 3 and 2.
We can think of factors as the smaller numbers that
multiply to give us the original number.
4-1 Factors and Prime Factorization
Helpful Hint
When the pairs of factors begin to repeat,
then you have found all of the factors of
the number you are factoring.
4-1 Factors and Prime Factorization
Example 1
List all of the factors of the number 16.
16
16 = 1 • 16
16 = 2 • 8
16 = 4 • 4
16 = 8 • 2
1 2 4
4
1
2
3
4
5
6
7
8
is a factor.
is a factor.
is not a factor.
is a factor.
is not a factor.
is not a factor.
is not a factor.
and 2 have already been listed so stop here.
8 16
You can draw a diagram to illustrate the
factor pairs.
The factors of 16 are 1, 2, 4, 8, and 16.
4-1 Factors and Prime Factorization
Example 2
List all of the factors of the number 19.
19
19 = 1 • 19
19 is not divisible by any
other whole number.
The factors of 19 are 1 and 19.
4-1 Factors and Prime Factorization
Example 3
List all of the factors of the number 12.
12
4-1 Factors and Prime Factorization
Example 4
List all of the factors of the number 11.
11
4-1 Factors and Prime Factorization
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.
The prime factorization of a number is
the number written as the product of its
prime factors.
4-1 Factors and Prime Factorization
Helpful Hint
You can use exponents to write prime
factorizations. Remember that an
exponent tells you how many times the
base is a factor.
4-1 Factors and Prime Factorization
Example 5
Write the prime factorization of 24.
Method 1: Use 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, or 23 • 3.
4-1 Factors and Prime Factorization
In Example 5, notice that the prime
factors may be written in a different order,
but they are still the same factors. Except
for changes in the order, there is only one
way to write the prime factorization of a
number.
4-1 Factors and Prime Factorization
Example 6
Write the prime factorization of 28.
Method 1: Use a factor tree.
Choose any two factors of 28 to begin. Keep finding
factors until each branch ends at a prime factor.
28
2
•
28
14
2
•
7
7
28 = 2 • 2 • 7
•
4
2
•
2
28 = 7 • 2 • 2
The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .
4-1 Factors and Prime Factorization
Communicator Activity
85
125
36
42
56
44
39
4-1 Factors and Prime Factorization
Do Now
List all the factors of each number.
1. 22
1, 2, 11, 22
2. 40
1, 2, 4, 5, 8, 10, 20, 40
3. 51
1, 3, 17, 51
Write the prime factorization of each number.
4. 32
25
5. 120 23  3  5
4-1 Factors and Prime Factorization
Objective:
•SWBAT find the greatest common factor
(GCF) of a set of numbers.
4-1 Factors and Prime Factorization
Question of the Day
Partner Activity
Victoria earned $49 on Friday, $42 on Saturday,
and $21 on Sunday selling bracelets. She sold
each bracelet for the same amount. What is
the most she could have charged for each
bracelet?
4-2 Greatest Common Factor
Factors shared by two or more whole numbers
are called common factors. The largest of the
common factors is called the greatest
common factor, or GCF.
Factors of 18:
1, 2, 3, 6, 9, 18
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 6
The greatest common factor (GCF) of 18 and 24
is 6.
There are several ways to find the greatest
common factor. This method is called the “listing
method”.
4-2 Greatest Common Factor
Example 1: Finding the GCF
Find the GCF of the set of numbers.
28 and 42
Method 1: List the factors.
factors of 28: 1, 2, 4, 7, 14, 28
List all the factors.
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Circle the GCF.
The GCF of 28 and 42 is 14.
4-2 Greatest Common Factor
TOYO
Find the GCF of the set of numbers.
18 and 36
Method 1: List the factors.
factors of 18:
factors of 36:
The GCF of 18 and 36 is 18.
4-2 Greatest Common Factor
Do Now
Find the GCF of the set of numbers using the
listing method.
1.) 16 and 28
2.) 24 and 36
4-2 Greatest Common Factor
Homework – pg. 153, #’s 1-3
Find the GCF of the set of numbers using the
listing method.
1.) 18 and 27
2.) 32 and 72
3.) 21, 42, and 56
4-2 Greatest Common Factor
Example 2: Finding the GCF
Find the GCF of the set of numbers.
18, 30, and 24
Method 2: Use the prime factorization.
18
30
24
4-2 Greatest Common Factor
18 = 2 • 3 • 3
30 = 2 • 3 • 5
24 = 2• 2 • 2 • 3
2•3 = 6
The GCF of 18, 30, and 24 is 6.
1-2 Divide Multi-Digit Whole Numbers
1.) What is the prime factorization of each
number?
2.) What are the common prime factors of ALL
the numbers?
3.) Did I multiply to get my GCF?
4-2 Greatest Common Factor
Let’s do this one together …
Find the GCF of the set of numbers using the
prime factorization method.
10, 20, and 30
1.) What is the prime factorization
of each number?
2.) What are the common prime
factors of each number?
The GCF of 10, 20, and
30 is 10.
3.) Did I multiply to get my GCF?
4-2 Greatest Common Factor
TOYO using prime factorization…
Find the GCF of the set of numbers.
40, 16, and 24
The GCF of 40, 16, and 24 is 8.
4-2 Greatest Common Factor
Exit Ticket
Find the greatest common factor of each
set of numbers. (Use any method)
1. 18 and 30
2. 8, 28, 52
3. 44, 66, 88
4-2 Greatest Common Factor
Do Now
Find the greatest common factor of each set of
numbers. You must use the prime factorization
method.
1.) 24, 36, and 96
4-2 Greatest Common Factor
Homework – Pg. 153, #’s 8-18 Even
Find the greatest common factor of each set of
numbers.
18.)
Ms.
Kline
makes
balloon
8.) 10
14.)
and
30,
35 45,
and
10.)
7536 andarrangements.
72 16.)12.)
16, 48,
16,She
and
40, has
and
72 32
88
blue balloons, 24 yellow balloons, and 16 white balloons.
Each arrangement must have the same number of each
color. What is the greatest number of arrangements that
Ms. Kline can make if every balloon is used?