Name ________________________________ Date __________________ Class _________________
CODE
60402
Practice A
Factors and Prime Factorization
List all of the factors of each number.
1. 6
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4. 12
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7. 16
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2. 9
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5. 21
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8. 25
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3. 10
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6. 18
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9. 31
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Write the prime factorization of each number.
10. 9
_______________________
13. 14
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16. 5
_______________________
11. 25
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14. 12
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17. 20
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12. 8
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15. 15
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18. 26
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19. There are 12 chairs in the meeting hall and an odd number of
tables. What are all the possible ways the chairs could be
arranged so that each table has the same number of chairs?
________________________________________________________________________________________
20. What are two different ways that 9 can be written as a product
of two numbers?
________________________________________________________________________________________
660402SR.docx
Name ________________________________ Date __________________ Class _________________
CODE
60402
Practice B
Factors and Prime Factorization
List all of the factors of each number.
1. 15
2. 24
3. 33
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________________________
________________________
_______________________
________________________
________________________
4. 72
5. 48
6. 95
_______________________
________________________
________________________
_______________________
________________________
________________________
7. 66
8. 87
9. 36
_______________________
________________________
________________________
_______________________
________________________
________________________
Write the prime factorization of each number.
10. 44
_______________________
13. 39
_______________________
16. 85
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11. 56
12. 42
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14. 36
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15. 125
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17. 100
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18. 32
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19. James has an assigned seat for his
flight to Denver. The seats on the
plane are numbered 1–49. James’s
seat number is an odd number
greater than 10 that is factor of 100.
What is his seat number for the flight?
20. Linda writes the prime factorization of
40 as 2 • 2 • 2 • 5 on the board. Phil
writes the prime factorization of 40 as
23 • 5. Who is correct?
_______________________________________
_______________________________________
660402SR.docx
Name ________________________________ Date __________________ Class _________________
CODE
60402
Practice C
Factors and Prime Factorization
List all of the factors of each number.
1. 92
2. 356
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3. 180
________________________________________
4. 550
_______________________________________
________________________________________
_______________________________________
________________________________________
Write the prime factorization of each number.
5. 225
_______________________
8. 216
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6. 333
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9. 423
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7. 124
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10. 810
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Write each number as a product in two different ways.
11. 81
12. 117
13. 375
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________________________
________________________
_______________________
________________________
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14. You and your friend are going to split the houses in your
neighborhood for newspaper delivery. Which would you prefer,
the odd-numbered houses or the prime-numbered houses? Explain.
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
15. Selma cannot remember her locker number! She knows that her
locker number is prime, and that it is a factor of 435. What are
all of Selma’s possible locker numbers?
________________________________________________________________________________________
660402SR.docx
Name ________________________________ Date __________________ Class _________________
CODE
60402
Review for Mastery
Factors and Prime Factorization
Factors of a product are the numbers that are multiplied to find that
product. A factor is also a whole number that divides the product
with no remainder.
To find all of the factors of 24, make a list of multiplication facts.
1 • 24 = 24
2 • 12 = 24
3 • 8 = 24
4 • 6 = 24
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Write multiplication facts to find the factors of each number.
1. 20
2. 16
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________________________________________
_______________________________________
________________________________________
3. 35
4. 31
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________________________________________
_______________________________________
________________________________________
A number written as the product of prime factors is called the prime
factorization of the number.
To write the prime factorization of 24, first write it as product of
2 numbers. Then rewrite each factor as the product of 2 numbers
until all of the factors are prime numbers.
24 = 4 • 6
(Write 24 as the product of 2 numbers.)
=2•2•6
(Rewrite 4 as the product of 2 prime numbers.)
=2•2•2•3
(Rewrite 6 as the product of 2 prime numbers.)
So, the prime factorization of 24 is 2 • 2 • 2 • 3 or 23 • 3.
Find the prime factorization of each number.
5. 28
_______________
660402SR.docx
6. 45
_______________
7. 50
________________
8. 72
________________
Name ________________________________ Date __________________ Class _________________
Challenge
CODE
60402
Prime Shades
For each given number, shade one box in each row of the table
to show a prime factor. Then use your shaded boxes to write
each number’s prime factorization.
1. 12
2. 70
3. 63
7
2
5
3
3
5
3
5
2
11
2
3
2
11
3
7
11
7
Prime factorization:
_______________________
4. 150
13
Prime factorization:
Prime factorization:
________________________
________________________
5
5. 84
11
7
6. 260
5
11
3
7
5
2
3
2
2
11
13
2
17
13
17
5
3
17
2
7
Prime factorization:
_______________________
7. 80
Prime factorization:
Prime factorization:
________________________
________________________
8. 1,750
17
5
9. 3,234
5
3
5
7
17
2
13
7
17
7
2
13
31
5
31
11
11
2
5
3
2
13
2
3
2
11
7
23
Prime factorization:
_______________________
660402SR.docx
Prime factorization:
Prime factorization:
________________________
________________________
Name ________________________________ Date __________________ Class _________________
CODE
60402
Problem Solving
Factors and Prime Factorization
Write the correct answer.
1. The area of a rectangle is the product
of its length and width. If a rectangular
board has an area of 30 square feet,
what are the possible measurements
of its length and width?
2. The first-floor apartments in Jenna’s
building are numbered 100 to 110.
How many apartments on that floor
are a prime number? What are those
apartment numbers?
_______________________________________
_______________________________________
_______________________________________
_______________________________________
3. A Russian mathematician named
Christian Goldbach came up with a
theory that every even number
greater than 4 can be written as the
sum of two odd primes. Test
Goldbach’s theory with the numbers 6
and 50.
4. Mr. Samuels has 24 students in his
math class. He wants to divide the
students into equal groups, and he
wants the number of students in each
group to be prime. What are his
choices for group sizes? How many
groups can he make?
_______________________________________
_______________________________________
_______________________________________
_______________________________________
Circle the letter of the correct answer.
5. Why is 2 the only even prime
number?
6. What prime numbers are factors of
both 60 and 105?
A It is the smallest prime number.
F 2 and 3
B All other even numbers are
divisible by 2.
G 2 and 5
C It only has 1 and 2 as factors.
J 5 and 7
H 3 and 5
D All odd numbers are prime.
7. If a composite number has the first
five prime numbers as factors, what is
the smallest number it could be?
A 30
8. Tim’s younger brother, Bryant, just
had a birthday. Bryant’s age only has
one factor, and is not a prime number.
How old is Bryant?
B 210
F 10 years old
C 2,310
G 7 years old
D 30,030
H 3 years old
J 1 year old
660402SR.docx
Name ________________________________ Date __________________ Class _________________
CODE
60402
Reading Strategies
Use an Organizer
A prime number has only two factors, 1 and the number itself.
2
2 • 1 = 2 The factors are 1 and 2.
A composite number has more than 2 factors.
6
1 • 6 = 6 and 2 • 3 = 6 The factors are 1, 2, 3, and 6.
When a composite number is written as the product of prime
numbers, it is called a prime factorization, such as 12 = 2 ⋅ 2 ⋅ 3.
Drawing a factor tree will help you find and organize the prime
factors of a number such as 42.
42
6
2
Write the number.
7
3
2⋅3⋅7
Write any pair of factors. Circle 7 because it is a
prime number.
Continue until all factors are prime.
Write the prime factors from least to greatest.
Answer each question.
1. Write a pair of factors you could use to find the prime factorization of 30.
________________________________________________________________________________________
2. Use the factors in the answer above to write the prime factorization of 30.
________________________________________________________________________________________
3. Make a factor tree for 36. What pair of factors did you start with?
________________________________________________________________________________________
4. What is the prime factorization of 36?
________________________________________________________________________________________
5. Make a factor tree for 16. What pair of factors did you start with?
________________________________________________________________________________________
6. What is the prime factorization for 16?
________________________________________________________________________________________
660402SR.docx
Name ________________________________ Date __________________ Class _________________
CODE
60402
Puzzles, Twisters & Teasers
Get Cooking
For each number in the left-hand column, there is matching prime
factorization in the right-hand column.
Use a straight edge to connect the numbers on the left to the
correct factorizations on the right. Each line will pass through a
letter in the center. Factorizations may be used more than once.
Fill in the letters below to solve the riddle.
1.
56
2.
225
3.
61
4.
294
5.
999
6.
77
7.
41
3⋅3⋅5⋅5
I
M
T
P
A
E
S
T
D
B
R
2⋅3⋅7⋅7
2⋅2⋅2⋅7
3 ⋅ 3 ⋅ 3 ⋅ 37
prime
2⋅3⋅3⋅3⋅5
7 ⋅ 11
What did the whole number serve at his family barbecue?
_______
_______
_______
_______
_______
4
6
2
1
3
_______
_______
_______
_______
6
2
7
5
660402SR.docx
CODE
60402
Answers
20. They both are.
LESSON 4-2
Practice C
Practice A
1. 1; 2; 3; 6
2. 1; 3; 9
3. 1; 2; 5; 10
4. 1; 2; 3; 4; 6;
12
5. 1; 3; 7; 21
6. 1; 2; 3; 6; 9;
18
7. 1; 2; 4; 8; 16
8. 1; 5; 25
9. 1; 31
10. 32
11. 52
12. 23
13. 2 • 7
14. 22 • 3
15. 3 • 5
16. 5
2
17. 2 • 5
18. 2 • 13
19. 12 chairs at 1 table or 4 chairs at 3
tables
20. Possible responses: 9 • 1; 1 • 9; 3 •
3
Practice B
1. 1; 3; 5; 15
2. 1; 2; 3; 4; 6;
8; 12; 24
3. 1; 3; 11; 33
4. 1; 2; 3; 4; 6; 8; 9;
12; 18; 24; 36; 72
5. 1; 2; 3; 4; 6; 8;
12; 16; 24; 48
6. 1; 5; 19; 95
7. 1; 2; 3; 6; 11;
22; 33; 66
8. 1; 3; 29; 87
9. 1; 2; 3; 4; 6; 9;
12; 18; 36
10. 22 • 11
12. 2 • 3 • 7
14. 22 • 32
16. 5 • 17
18. 25
660402SR.docx
1. 1; 2; 4; 23; 46; 92
2. 1; 2; 4; 89; 178; 356
3. 1; 2; 3; 4; 5; 6; 9; 10; 12; 15;
18; 20; 30; 36; 45; 60; 90; 180
4. 1; 2; 5; 10; 11; 22; 25; 50;
55; 110; 275; 550
5. 32 • 52
6. 32 • 37
7. 22 • 31
8. 23 • 33
9. 32 • 47
10. 2 • 34 • 5
Possible answers given:
11. 1 • 81; 9 • 9; 3 • 27
12. 1 • 117; 3 • 39; 9 • 13
13. 1 • 375; 3 • 125; 5 • 75; 15 • 25
14. If students want more houses, they
should choose odd numbers. If they
want fewer houses, they should
choose prime numbers, because
there are fewer prime numbers than
odd numbers.
15. 3, 5, or 29
Review for Mastery
1. 1 • 20 = 20; 2 • 10 = 20; 4 • 5 = 20
2. 1 • 16 = 16; 2 • 8 = 16; 4 • 4 = 16
3. 1 • 35 = 35; 5 • 7 = 35
4. 1 • 31 = 31
5. 22 • 7
7. 2 • 52
11.
13.
15.
17.
19.
23 • 7
3 • 13
53
22 • 52
25
Challenge
1.
7
2
3
5
2
11
6. 32 • 5
8. 23 • 32
22 • 3
2.
5
3
2
11
3
7
2•5•7
3.
3
5
2
3
11
7
32 • 7
4.
13
5
3
7
2
11
17
5
2 • 3 • 52
5.
11
7
5
2
13
2
3
17
2
2 •3•7
6.
5
11
3
2
17
13
2
7
22 • 5 • 13
7.
5
7
13
7
31
5
5
3
2
11
3
2•5 •7
9.
5
3
17
7
31
11
2
13
7
23
2 • 3 • 72 • 11
Problem Solving
1. 1, 2, 3, 5, 6, 10, 15, or 30 feet
2. 4 apartments; 101, 103, 107, and
109
3. Possible answers: 6 = 3 + 3; 50 = 19
+ 31
4. 12 groups of 2 students each or 8
groups of 3 students each
5. B
6. H
7. C
8. J
Reading Strategies
1. 5 and 6, 3 and 10, or 2 and 15
2. 2 ⋅ 3 ⋅ 5 = 30
3. Possible answers: 9 and 4 or 6 and
6
4. 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36
5. Possible answers: 4 and 4 or 8 and
2
6. 2 ⋅ 2 ⋅ 2 ⋅ 2 = 16
Puzzles, Twisters, and Teasers
17
2
2
13
1. 2 ⋅ 2 ⋅ 2 ⋅ 7 (M)
2. 3 ⋅ 3 ⋅ 5 ⋅ 5(I)
11
2
3. prime (E)
4. 2 ⋅ 3 ⋅ 7 ⋅ 7(P)
2
3
24 • 5
8.
17
660402SR.docx
5
5. 3 ⋅ 3 ⋅ 3 ⋅ 37 (S)
7. prime (B)
PRIME RIBS
6. 7 ⋅ 11 (R)