4-2 Factors and Prime Factorization
Learn to write prime factorizations of
composite numbers.
Course 1
4-2 Factors
Insert Lesson
TitleFactorization
Here
and Prime
Vocabulary
factor
prime factorization
Course 1
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
Course 1
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.
Course 1
2-5 Greatest Common Factor
T-Chart/ Prime Factorization Method
36
12
1
2
3
Course 2
12
6
1
2
36
18
4
3
4
6
12
9
6
O
O
54
1
2
3
6
O
54
27
18
9
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.
Course 1
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.
Course 1
4-2 Factors and Prime Factorization
Additional Example 2A: Writing Prime
Factorizations
Write the prime factorization of each number.
A. 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
24
2
•
2
•
6
12
•
6
2
•
3
3
•
2
4
2
•
2
24 = 3 • 2 • 2 • 2
24 = 2 • 2 • 2 • 3
3
The prime factorization of 24 is 2 • 2 • 2 • 3, or 2 • 3 .
Course 1
4-2 Factors and Prime Factorization
Additional Example 2B: Writing Prime
Factorizations
Write the prime factorization of each number.
B. 42
Method 1: Use a ladder diagram.
Choose a prime factor of 42 to begin. Keep dividing by
prime factors until the quotient is 1.
3
42
2
14
2
7
7
1
42 = 3 • 2 • 7
42
21
3
7
7
1
42 = 2 • 3 • 7
The prime factorization of 42 is 2 • 3 • 7.
Course 1
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.
Course 1
4-2 Factors and Prime Factorization
Try This: Example 2A
Write the prime factorization of each number.
A. 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
28
2
•
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 .
Course 1
4-2 Factors and Prime Factorization
Try This: Example 2B
Write the prime factorization of each number.
B. 36
Method 1: 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.
Course 1
4-2 Factors
Insert Lesson
and Prime
TitleFactorization
Here
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
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3
5