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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Finding Factors
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
______________________________________________________
2. In 3 3 4 5 12, which number is the product? _______
3. A factor is a number that is _________________________ by
another number to give a ____________________ .
4. In 3 3 4 5 12, which numbers are the factors? ________________
5. Three ways shown to represent 12 using numbers are:
______________________________________________________
______________________________________________________
______________________________________________________
Key Words:
Factor
Area of a rectangle
Unit square
Commutative
Property of
Multiplication
Multiplication
Property of 1
Learning
Objectives:
¥ Use an area model
to represent
multiplication.
¥ Demonstrate that
multiplication is
commutative.
¥ Find the pairs of
factors of a whole
number.
¥ Recognize that any
number has 1 and
itself as factors.
6. Area is the number of __________ _______________ in a
____________ surface.
7. The area of a rectangle is equal to its _______________
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multiplied by its _______________ .
8. We can also use 3 groups of _____ unit squares to get 12.
9. The Commutative Property of Multiplication states that if the
positions of two or more ________________ are changed, their
___________ remains the same.
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Name ___________________________________
Date ________________________
10. Three different pairs of factors for 12 are _____ 3 _____ ,
_____ 3 _____ , and _____ 3 _____ .
11. Four different
factor pairs
for 42 are:
Length (units) 3 Width (units) 5
1
3
2
Area
5
42
3
5
42
3
3
5
42
6
3
5
42
42
12. Neither 4 nor 5 can be a factor of 42 because
________________
______________________________________________________
____________________________________________________ .
13. The number 42 has _____ different pairs of factors.
14. The factors common to both 12 and 42 are _____, _____, _____,
and _____ . _____ is the lowest common factor of 12 and 42.
15. The Multiplication Property of One states that _______ times any
number equals that ____________________ .
3 and _____
_____ and 6
2 and _____
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16. The factor pairs of 24 are:
1 and _____
17. The factors of a number are always either less than or
____________ ____________ the number.
Destination
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Finding Factors
1. Use numbers to show three ways to represent 18.
____________
______________________________________________________
______________________________________________________
2. Each square represents 1 square unit. Fill in the missing
information.
Length 5 __________ units
Width 5 __________ units
Area 5 __________ square units
3. Explain how you know that these two rectangles have the same
area.
____________________
____________________
____________________
____________________
______________________________________
______________________________________________________
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______________________________________________________
4. Complete each number sentence. Then tell what property the
number sentence represents.
a. 3 3 ____ 5 5 3 ____ ________________________________
____________________________________________________
b. 18 3 ____ 5 18 ______________________________________
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Name ___________________________________
Date ________________________
5. Tim and Shandra are making a garden that is shaped like a
rectangle. Its area is 28 square units. Use what you know about
all factor pairs to draw the different rectangles Tim and Shandra
could make. Label the length and width of each rectangle.
6. Write all of the pairs of factors for each whole number. Then tell
how many different factor pairs there are.
Whole
Number
Factor Pairs
Number of
Different Pairs
20
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30
57
Destination
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Prime and Composite
Numbers
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
______________________________________________________
2. The Multiplication Property of One states that ______ times any
number equals that number.
Key Words:
Prime number
Composite number
Divisible
Factor
Factor pairs
Factor tree
Learning
Objectives:
¥ Identify the prime
numbers less
than 50.
3. The number 1 has _____ and _____ as a factor pair. Since the
¥ Determine the
prime factors in
a number.
two factors are the same, there are _____ different factors for 1.
4. The number 4 has only 3 different factors and these factor pairs:
_____ 3 _____ and _____ 3 _____.
5. All whole numbers greater than 1 have at least _______ different
factors.
6. A prime number is a number that has exactly ________ different
factors, _______ and _______________ .
7. The prime numbers from 1 to 12 are: _____ , _____ , _____ ,
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_____ , and _____ .
8. Draw a circle around each of the numbers below that have 2 as a
factor. Draw a square around the numbers that have 3 as a
factor. Draw a triangle around the numbers that are prime.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
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Name ___________________________________
Date ________________________
9. List the numbers from 2 to 30 that have both 2 and 3 as factors.
______________________________________________________
10. What are the prime numbers between 30 and 50? ____________
_____________________________________________________
11. A ________________________ number is a counting number
greater than 1 that is not prime.
12. The number 1 is neither ________________ nor _____________.
It is the only counting number with just _____ factor.
13. Every composite number is the product of two or more
_________________ ____________________ .
14. Complete these
factor trees to
show the prime
factors of 16.
16
16
2 3 8
4
3
3
3
4
3
3
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15. Rewrite 100 as a product of its prime factors.
_____ 3 _____ 3 _____ 3 _____
16. By looking at the factors of a number, you can tell whether it is
a prime or a ____________________ number.
Destination
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Prime and Composite
Numbers
1. List all the factor pairs for each of the numbers 11 to 20. Then
give the number of different factors for each number.
Different Factor Pairs
Number of Different
Factors
11
12
13
14
15
16
17
18
19
20
2. Complete the factor tree.
45
5
3
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3
9
3
3. Starting with a factor pair other than 5 and 9, make a different
factor tree for 45.
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Name ___________________________________
Date ________________________
4. Why is the final set of factors the same in both factor trees for 45?
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
5. Use the space below to make two different factor trees for 48.
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6. List the factor pairs for 36. Then sort the factors into prime and
composite numbers.
Factors of 36: __________________________________________
Prime Factors
Composite Factors
Destination
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Identifying Common Factors
As you work through the tutorial, complete the following questions.
1. What is your mission for this lesson? ________________________
________________________________________________________
Key Words:
Prime number
Composite number
Venn diagram
Common factor
Greatest Common
Factor
2. Is 12 a prime factor of 24? ______ Why or why not? ____________
______________________________________________________
______________________________________________________
Learning
Objectives:
¥ Find the common
factors of two
whole numbers.
4. The prime factorization of 24 is _____ 3 _____ 3 _____ 3 _____ .
¥ Use factor trees
and a Venn
diagram to identify
the Greatest
Common Factor
of two 2-digit
numbers.
5. A _________________ diagram is used to display objects that
have certain properties in common.
¥ Find the Greatest
Common Factor
of two 3-digit
numbers.
3. ____________ ________________________ is writing a number
as a product of its prime factors.
6. The prime factorization of 40 is _____ 3 _____ 3 _____ 3 _____ .
7. The prime factors that 24 and 40 have in common are _____ ,
_____ , and _____ .
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8. What do you know about the numbers that appear in the region of
a Venn diagram where the loops overlap? ____________________
______________________________________________________
9. In this Venn diagram, the overlapping
24
40
region shows the prime ____________
common to _______ and __________ .
3
2
2 2
5
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Name ___________________________________
Date ________________________
10. The GCF, or ________________ ________________
________________, is the greatest factor that two or more
numbers have in common.
11. The GCF of 24 and 40 is _____ 3 _____ 3 _____ , or _____ .
12. Use these factor trees to find the prime factors of 400 and 225.
400
225
5 3
2 3
3 9
2 3
2 3
3
2 3
13. The common prime factors of 400 and 225 are _____ and _____ .
14. The GCF of 400 and 225 is _____ 3 _____ , or _______ .
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Destination
Math
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Identifying Common Factors
1. Use these factor trees to find the prime factorizations of 36
and 48.
36
6
3
3
48
6
4
3
3
3
12
3
3
Prime factorization of 36: __________________________________
Prime factorization of 48: __________________________________
2. Use this Venn diagram to show the prime factors of 36 and 48.
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3. The Greatest Common Factor of 36 and 48 is ________________ .
Explain how you found your answer. ________________________
______________________________________________________
______________________________________________________
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Name ___________________________________
Date ________________________
4. Use a Venn diagram or a factor tree to find the Greatest Common
Factor of 54 and 72. ___________.
5. Use the space below to make a factor tree for the prime
factorizations of 220 and 620.
6. What prime factors do 220 and 620 have in common?
______________________________________________________
7. Find the GCF of 220 and 660. Show your work. ______________
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______________________________________________________
8. Is the GCF of two numbers always, sometimes, or never a prime
number? _________________________ Explain your answer.
______________________________________________________
______________________________________________________
Destination
Math
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
Finding Factors
1. Write all of the factor pairs for 32. __________________________
______________________________________________________
a. How many different factor pairs are there? _____
b. Why do factor pairs such as 2 3 16 and 16 3 2 count as one
pair of factors instead of as two different pairs of factors?
____________________________________________________
____________________________________________________
Prime and Composite Numbers
2. Use the space on the right
to make a factor tree for 60.
Circle the prime factors.
3. Sort the following numbers into two groups, prime numbers and
composite numbers. Explain how you sorted.
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3, 8, 15, 17, 23, 27, 31, 39, 43, 49
Prime numbers: ________________________________________
Composite numbers: ____________________________________
______________________________________________________
______________________________________________________
Destination
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Name ___________________________________
Date ________________________
Identifying Common Factors
4. Get ready to write the prime factorization for each of two numbers.
a. Prime factorization of 30: ____________________________
Prime factorization of 42: _____________________________
b. Complete the Venn diagram
to show the prime
factorizations of 30 and 42.
30
42
c. Which prime factors are common to both 30 and 42? ________
d. The GCF of 30 and 42 is _____________________ .
Putting It All Together
a. If Terri uses all of the red and gold beads, she can make
________ identical bracelets.
b. Each bracelet will have _____ red beads and _____ gold
beads.
c. Explain. ________________________________________
________________________________________________
________________________________________________
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5. Terri is making bracelets from blue, red, and gold beads. She
has a lot of blue beads, but she has only 42 red beads and 48
gold beads. Terri wants all the bracelets to have an equal
number or red beads and an equal number of gold beads.
Destination
Math
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Name ___________________________________
Date ________________________
COURSE: MSC III
MODULE 1: Numbers and Number Sense
UNIT 2: Numbers as Factors
1. Clint spots the following numbers of birds over the weekend.
Friday: 24 birds
Saturday: 64 birds
Sunday: 48 birds
In science class, he makes a chart to record the birds he saw.
Clint uses a bird symbol to stand for a certain number of birds. For
example,
could equal 2 birds.
a. What is the greatest number that one bird symbol can
represent? ________ Explain. __________________________
____________________________________________________
____________________________________________________
b. If Clint uses the number found above, how many bird symbols
should he use for Friday? _____ Saturday? _____ Sunday? _____
2. Complete each number sentence. Then tell what property each
number sentence represents.
a. 8 3 ____ 5 4 3 ____
________________________________
____________________________________________________
b. 11 3 ____ 5 11 ______________________________________
3. Use the clues below to identify a mystery number.
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Clue 1: It is greater than 10 and less than 25.
Clue 2: It is 3 less than a prime number.
Clue 3: It has six different factors.
The number is _____ . Explain how you found your answer.
______________________________________________________
______________________________________________________
______________________________________________________
Destination
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Name ___________________________________
Date ________________________
4. A 6-sectioned spinner has these numbers on it: 10, 18, 22, 25, 42,
and 72. If the spinner lands on a number with the greatest or
least number of prime factors, a player earns 10 points. What
numbers must a player spin to earn 10 points? ________ Explain.
______________________________________________________
______________________________________________________
______________________________________________________
5. Use a Venn diagram to show the prime factors of 24, the prime
factors of 42, and the prime factors common to 24 and 42.
6. Sonya draws these three numbers from a stack of number cards:
350, 480, and 630. To win a round in a math game, Sonya needs
to identify the pair of numbers with the largest GCF. Which two
numbers does Sonya need to identify? Use factor trees to find
your answer. _______ _______
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Destination
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