The document is a lesson on representing numbers in different ways through factors and prime factorization. It defines key vocabulary like factor and prime factorization. It provides examples of finding all the factors of a number and using a factor tree to write the prime factorization by decomposing a number into prime factors. Students are guided through examples and practice problems to find the factors and prime factorizations of various numbers.

1. Name ________________________________ Date _________________
Mrs. Labuski / Mrs. Portsmore Per ________ Unit 4 Lesson 2 Factors & Prime Factorization
TB 4-2
Essential Question: Why do we represent numbers in different ways?
VOCABULARY DEFINTION EXAMPLE
Factor
Prime Factorization
List all of the factors of each number.
18 = 1•18
18 = 2•9
18 = 3•6
The factors of 18 are: 1, 2, 3, 6, 9, 18
Now you try:
What divisibility
rules can help you?
12: ________________________________________________ ____
What divisibility
21: ________________________________________________ rules can help you?
____
16: _________________________________________________ What divisibility
rule can help
you? ____

2. To find the Prime Factorization of each number use a Factor Tree
36
1. Choose any two factors of the number: 3 •12
2. Circle the prime number 2•6
3. Keep finding factors until each branch ends in a prime number 2 •3
4. Rewrite the factors in order 36= 3•2•2• 3
5. Combine any factors into exponential form 36= 22 • 32
Now let’s try one together: What divisibility
rule can help
1. 28 What divisibility 2. 45 you? ____
rule can help
you? ____
____________________ ____________________
What divisibility
rule can help
What divisibility you? ____
3. 50 rule can help 4. 72
you? ____
____________________ ____________________

3. Name ________________________________ Date _________________
Mrs. Labuski / Mrs. Portsmore Per ________ Unit 4 Lesson 2 Factors & Prime Factorization
TB 4-2
Essential Question: Why do we represent numbers in different ways?
VOCABULARY DEFINTION EXAMPLE
Whole numbers
that are multiplied 2 •3 = 6
Factor
together to find a factors
product
Is when a number is
written as the 12 =
Prime Factorization
product of its prime 3•2•2
factors
List all of the factors of each number.
18 = 1•18
18 = 2•9
18 = 3•6
The factors of 18 are: 1, 2, 3, 6, 9, 18
Now you try:
12: __1,2,3,4,6________________________________________
21: __1,3,7,21_________________________________________
16: __1,2,4,8,16________________________________________

4. To find the Prime Factorization of each number use a Factor Tree
36
6. Choose any two factors of the number: 3 •12
7. Circle the prime number 2•6
8. Keep finding factors until each branch ends in a prime number 2 •3
9. Rewrite the factors in order 36= 3•2•2• 3
10. Combine any factors into exponential form 36= 22 • 32
Now let’s try one together:
2. 28 2. 45
2 14 5 9
2 7 3 3
22 •7 32 •5
____________________ ____________________
3. 50 4. 72
5 10 8 9
2 5 2 4 3 3
2 2
2 • 52 23 • 32
____________________ ____________________