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4-2 Factors and Prime Factorization
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-2 Factors and Prime Factorization
Warm Up
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
4-2 Factors and Prime Factorization
Problem of the Day
At the first train stop, 7 people disembarked. At
the second stop, 8 people disembarked. At the
fourth stop, the last 6 people disembarked. If
there were 28 people on the train before the first
stop, how many people left at the third stop?
7 people left at the third stop
4-2 Factors and Prime Factorization
Learn to write prime factorizations of
composite numbers.
4-2 Factors and Prime Factorization
Vocabulary
factor
prime factorization
4-2 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.
4-2 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.
4-2 Factors and Prime Factorization
Additional Example 1A: Finding Factors
List all of the factors of the number 16.
A. 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.
4-2 Factors and Prime Factorization
Additional Example 1B: Finding Factors
List all of the factors of the number 19.
B. 19
19 = 1 • 19
19 is not divisible by any
other whole number.
The factors of 19 are 1 and 19.
4-2 Factors and Prime Factorization
Check It Out: Example 1A
List all of the factors of the number 12.
A. 12
12
12
12
12
=
=
=
=
1 2 3
1
2
3
4
•
•
•
•
12
6
4
3
1 is a factor.
2 is a factor.
3 is a factor.
4 and 3 have already been listed
so stop here.
4 6 12
You can draw a diagram to
illustrate the factor pairs.
The factors of 12 are 1, 2, 3, 4, 6, and 12
4-2 Factors and Prime Factorization
Check It Out: Example 1B
List all of the factors of the number 11.
B. 11
11 = 1 • 11
11 is not divisible by any
other whole number.
The factors of 11 are 1 and 11.
4-2 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.
4-2 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.
4-2 Factors and Prime Factorization
Additional Example 2A: Writing Prime Factorizations
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.
4-2 Factors and Prime Factorization
Additional Example 2B: Writing Prime Factorizations
Write the prime factorization of 45.
Method 2: Use a ladder diagram.
Choose a prime factor of 45 to begin. Keep dividing by
prime factors until the quotient is 1.
3
45
5
15
3
5
5
1
45 = 3 • 3 • 5
45
9
3
3
3
1
45 = 5 • 3 • 3
The prime factorization of 45 is 3 • 3 • 5 or 32 • 5 .
4-2 Factors and Prime Factorization
In Example 2, 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.
4-2 Factors and Prime Factorization
Check It Out: Example 2A
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 .
4-2 Factors and Prime Factorization
Check It Out: Example 2B
Write the prime factorization of 36.
Method 2: Use a ladder diagram.
Choose a prime factor of 36 to begin. Keep
dividing by prime factors until the quotient is 1.
3
36
3
12
2
3
12
3
6
2
36
4
2
3
1
36 = 3 • 2 • 2 • 3
2
2
1
36 = 3 • 3 • 2 • 2
The prime factorization of 36 is 3 • 2 • 2 • 3, or 32 • 23.
4-2 Factors and Prime Factorization
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-2 Factors and Prime Factorization
Lesson Quiz
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
4-2 Factors and Prime Factorization
Lesson Quiz for Student Response Systems
1. Which of the following lists all the
factors of 33?
A. 1, 2, 11, 22
B. 2, 22
C. 3, 11
D. 1, 3, 11, 33
4-2 Factors and Prime Factorization
Lesson Quiz for Student Response Systems
2. Which of the following lists all the
factors of 30?
A. 1, 2, 3, 4, 5, 6, 7, 30
B. 1, 2, 3, 5, 6, 10, 15, 30
C. 5, 7, 10, 12, 15
D. 4, 8, 12, 13, 17
4-2 Factors and Prime Factorization
Lesson Quiz for Student Response Systems
3. Which of the following lists all the
factors of 14?
A. 1, 4, 14
B. 1, 7, 14
C. 1, 2, 7, 14
D. 1, 2, 4, 14
4-2 Factors and Prime Factorization
Lesson Quiz for Student Response Systems
4. Identify the prime factorization of 625.
A. 34
B. 33  5
C. 3  53
D. 54
4-2 Factors and Prime Factorization
Lesson Quiz for Student Response Systems
5. Identify the prime factorization of 90.
A. 2  32  5
B. 22  32  5
C. 2  32  52
D. 22  32  52