Unit 2: Factors & Multiples

ANSWER KEY

The following unit includes:

Prime Factorization

Greatest Common Factor

Least Common Multiple

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Math in Demand

with

Teacher Notes: Provided in this file is the answer key for Unit 2. There

are a few things that you might find helpful:

(1) You can differentiate for your students by deciding to print the blank template or answer key. I like to use

direct instruction and have my students fill in the blank template. However, I accommodate any of my students that have difficulty writing by providing the answer key.

(2) If you feel that I left anything out, you can ALWAYS have students add any additional notes. Every teacher

likes to teach a concept differently than another.

(3) You can use colored paper when printing the cutouts. This makes it less for students to color and it still

makes the page look colorful! Also, have students color code important info with highlighters!! It looks great!

(4) You can print the interactive notebook at 90% to make it fit into a smaller composition notebook.

If you have any questions, please don’t hesitate to email me at jen_marie_18@hotmail.com. Thank you so much!

Math in Demand

Unit 2 Checklist

(Factors and Multiples) As you go through the unit, check off the concepts that you have mastered. Leave the other ones unchecked so that you know which concepts you need to study before a test!

The following unit includes:

□ Prime Factorization

□ Greatest Common Factor

□ Least Common Multiple

©2016 Math in Demand

©2016 Math in Demand

Unit 2 Overview (Factors and Multiples)

Concepts(s):

Essential Questions:

Vocabulary:

Important Dates: Pre-Test: Post-Test: Vocabulary Quiz:

Scores: Pre-Test: Post-Test: Vocabulary Quiz:

Prime Factorization

Prime Numbers

Greatest Common Factor

Least Common Multiple

Why do we break down numbers to their prime factorization?

When do we need to determine the greatest common factor?

When do we need to determine the least common multiple?

Prime Factorization

Greatest Common Factor

Least Common Multiple

This overview shows you important information that you will be learning throughout the

unit. Make sure to fill out important dates and scores!

Factors and Multiples (Prime Factorization)

©2016 Math in Demand

I can ___________________

_______________________

What is prime factorization?

Example: What is the prime factorization of 54?

The prime factorization of 54 is: 2 ∙ 3 ∙ 3 ∙ 3 = 2 ∙ 33

54

2 27

3 9

3 3

break down numbers to

their prime factorization.

The set of prime numbers that when multiplied together will give the original number.

What

is the

facto

r

tree

of 4

2?

Directions: Cut out the following figure on the dotted lines. Fold on the solid line. Glue the figure on the area that says “Glue Here”.

What

is the

facto

r

tree

of 4

2?

Directions: Cut out the following figure on the dotted lines. Fold on the solid line. Glue the figure on the area that says “Glue Here”.

©2016 Math in Demand

Factors and Multiples (Prime Factorization)

1.) Prime factorization of 48

48 = 2∙2∙2∙2∙3 = 24 ∙ 3

2.) Prime factorization of 60

60 = 2∙2∙3∙5 = 22 ∙ 3 ∙ 5

3.) Prime factorization of 96

96 = 2∙2∙2∙2∙2∙3 = 25 ∙ 3

Reflection: I learned…

©2016 Math in Demand

On a rating of 1-5, how comfortable are you with this concept?

(5 is the highest)

1 2 3 4 5

Answer

Answer

Answer

24∙3

22∙3∙5

25 ∙ 3

Factors and Multiples (Greatest Common Factor)

©2016 Math in Demand

I can ___________________

_______________________

What is the great common factor?

The greatest common factor (GCF) is the biggest number that is divisible by both numbers.

Example:

Glue Here

What is the greatest common factor of 20 and 28?

The greatest common factor of 20 and 28 is: 4

Factors of 20

5 10 20

Factors of 28

7 14 28

Both

1 2 4

determine the greatest

common factor of two numbers.

©2016 Math in Demand

Greatest Common Factor

Factors of 20

Factors of 28

BO

TH

Directions: Cut out the following figure on the dotted lines. Fold on the solid line. Glue the figure on the area that says “Glue Here”.

Factors and Multiples (Greatest Common Factor)

1.) Determine the GFC of 36 and 54.

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

2.) Determine the GFC of 12 and 21.

Factors of 12 = 1, 2, 3, 4, 6, 12 Factors of 21 = 1, 3, 7, 21

3.) Determine the GFC of 18 and 36.

Factors of 18 = 1, 2, 3, 6, 9, 18 Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Reflection: I learned…

©2016 Math in Demand

On a rating of 1-5, how comfortable are you with this concept?

(5 is the highest)

1 2 3 4 5

Answer

Answer

Answer

18

3

18

Factors and Multiples (Least Common Multiple)

I can ___________________

_______________________

©2016 Math in Demand

What is the least common multiple?

The least common multiple (LCM) is the smallest multiple that is divisible by both of the numbers.

Example: What is the least common factor of 6 and 8?

Glue

Here

6 12 18 24 30

8 16 24 32 40 24

6 ∙ 1 =

6 ∙ 2 =

6 ∙ 3 =

6 ∙ 4 =

6 ∙ 5 =

= 8 ∙ 1 = 8 ∙ 2

= 8 ∙ 3

= 8 ∙ 4

= 8 ∙ 5

You can also use a Venn Diagram!

6

8

determine the least

common multiple of two numbers.

6 12 18 30

8 16 32 40

24

6

8

What is the LCM of 6

and 8?

What is the LCM of 6

and 8?

Directions: Cut out the following figure on the dotted lines. Fold on the solid line. Glue the figure on the area that says “Glue Here”.

6

8

What is the LCM of 6

and 8?

What is the LCM of 6

and 8?

Directions: Cut out the following figure on the dotted lines. Fold on the solid line. Glue the figure on the area that says “Glue Here”.

©2016 Math in Demand

Factors and Multiples (Least Common Multiple)

Reflection: I learned…

1.) Determine the LCM of 5 and 8.

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40,…

Multiples of 8 = 8, 16, 24, 32, 40, 48,…

2.) Determine the LCM of 9 and 12.

Multiples of 9 = 9, 18, 27, 36, 45,…

Multiples of 12 = 12, 24, 36, 48,…

3.) Determine the LCM of 11 and 13.

Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, …

Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, …

Answer

Answer

Answer

©2016 Math in Demand

On a rating of 1-5, how comfortable are you with this concept?

(5 is the highest)

1 2 3 4 5

40

36

143

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