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Name
LESSON
Date
Class
Practice B
4-2 Factors and Prime Factorization
List all the factors for each number.
1. 15
2. 24
3. 33
4. 72
5. 48
6. 95
7. 66
8. 87
9. 36
Write the prime factorization of each number.
10. 44
11. 56
12. 42
13. 39
14. 36
15. 125
16. 85
17. 100
18. 32
19. James has an assigned seat for his
20. Linda writes the prime factorization of
flight to Denver. The seats on the
40 as 2 • 2 • 2 • 5 on the board. Phil
plane are numbered 1–49. James’s
writes the prime factorization of 40 as
seat number is an odd number greater
23 • 5. Who is correct?
than 10 that is factor of 100. What is
his seat number for the flight?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Middle School Math Course 1
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Practice B
4-2 Factors and Prime Factorization
Practice A
4-2 Factors and Prime Factorization
LESSON
LESSON
List all the factors for each number.
List all the factors for each number.
1. 6
2. 9
1. 15
3. 10
2. 24
3. 33
1; 3; 5; 15
1; 2; 3; 6
4. 12
1; 3; 9
1; 2; 3; 4; 6; 12
8; 12; 24
6. 18
1; 3; 7; 21
1; 2; 3; 6; 9; 18
8. 25
1; 2; 4; 8; 16
4. 72
9. 31
1; 5; 25
1; 31
Write the prime factorization of each number.
10. 9
13. 14
6. 95
1; 2; 3; 4; 6; 8;
12; 18; 24; 36; 72
12; 16; 24; 48
12. 8
23
1; 5; 19; 95
8. 87
1; 2; 3; 6; 11;
52
14. 12
9. 36
1; 3; 29; 87
1; 2; 3; 4; 6; 9;
22; 33; 66
12; 18; 36
15. 15
22 • 3
2•7
16. 5
5. 48
1; 2; 3; 4; 6; 8; 9;
7. 66
11. 25
32
1; 3; 11; 33
1; 2; 5; 10
5. 21
7. 16
1; 2; 3; 4; 6;
Write the prime factorization of each number.
3•5
17. 20
10. 44
2
5
11. 56
22 • 11
18. 26
2 •5
13. 39
2 • 13
15. 125
22 • 32
16. 85
18. 32
22 • 52
Possible responses: 9 • 1; 1 • 9; 3 • 3
25
19
Holt Middle School Math Course 1
Holt Middle School Math Course 1
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.
2. 356
1; 2; 4; 89; 178; 356
3. 180
20
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
LESSON
List all the factors for each number.
1; 2; 4; 23; 46; 92
They both are.
Reteach
4-2 Factors and Prime Factorization
Practice C
4-2 Factors and Prime Factorization
LESSON
1. 92
25
19. James has an assigned seat for his
20. Linda writes the prime factorization of
flight to Denver. The seats on the
40 as 2 • 2 • 2 • 5 on the board. Phil
plane are numbered 1–49. James’s
writes the prime factorization of 40 as
seat number is an odd number greater
23 • 5. Who is correct?
than 10 that is factor of 100. What is
his seat number for the flight?
20. What are two different ways that 9 can be written as a product of
two numbers?
Copyright © by Holt, Rinehart and Winston.
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53
17. 100
5 • 17
12 chairs at 1 table or 4 chairs at 3 tables
2•3•7
14. 36
3 • 13
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?
12. 42
23 • 7
To find all of the factors of 24, make a list of multiplication facts.
4. 550
1; 2; 3; 4; 5; 6; 9; 10; 12; 15;
1; 2; 5; 10; 11; 22; 25; 50
18; 20; 30; 36; 45; 60; 90; 180
55; 110; 275; 550
1 • 24
2 • 12
3•8
4•6
24
24
24
24
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Write the prime factorization of each number.
5. 225
Write multiplication facts to find the factors of each number.
6. 333
32 • 5 2
8. 216
7. 124
32 • 37
9. 423
23 • 3 3
1. 20
22 • 31
10. 810
32 • 47
1 • 20 20; 2 • 10 20;
1 • 16 16; 2 • 8 16;
4 • 5 20
4 • 4 16
2 • 34 • 5
Write each number as a product in two different ways.
Possible answers given.
11. 81
13. 375
12. 117
2. 16
1 • 81; 9 • 9;
1 • 117; 3 • 39;
1 • 375; 3 • 125;
3 • 27
9 • 13
5 • 75; 15 • 25
3. 35
4. 31
1 • 35 35; 5 • 7 35
1 • 31 31
A number written as the product of prime factors is called the prime
factorization of the number.
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.
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.
If students want more houses, they should choose odd 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.)
If they want fewer houses, they should choose prime numbers,
because there are fewer prime numbers than odd numbers.
So, the prime factorization of 24 is 2 • 2 • 2 • 3 or 23 • 3.
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?
Find the prime factorization of each number.
3, 5, or 29
5. 28
22 • 7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
21
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 1
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
106
6. 45
7. 50
32 • 5
8. 72
2 • 52
22
23 • 32
Holt Middle School Math Course 1
Holt Middle School Math
Course 1