12
16
20
1�4 2�4 3�4 4�4 5�4
8
39
1
,
,
,
,
↑
↑
↑
↑
↑
1�3
2�3
3�3
4�3
5�3
The first five multiples of 3 are:
3
List the first five multiples of the number.
Try These
The first five multiples of 4 are:
4, 8, 12, 16, 20.
0
4
List the first five multiples of 4.
Multiply 4 by the numbers
1, 2, 3, 4, and 5.
21
28
35
1�7 2�7 3�7 4�7 5�7
14
2
,
,
,
,
↑
↑
↑
↑
↑
1�2
2�2
3�2
4�2
5�2
The first five multiples of 2 are:
2
The first five multiples of 7 are:
7, 14, 21, 28, 35.
0
7
List the first five multiples of 7.
Multiply 7 by the numbers
1, 2, 3, 4, and 5.
A multiple is the product of a number and any whole number except zero.
Multiples
© Houghton Mifflin Harcourt Publishing Company
27
36
45
1�9 2�9 3�9 4�9 5�9
18
3
Go to the next side.
,
,
,
,
↑
↑
↑
↑
↑
1�6
2�6
3�6
4�6
5�6
The first five multiples of 6 are:
6
The first five multiples of 9 are:
9, 18, 27, 36, 45.
0
9
List the first five multiples of 9.
Multiply 9 by the numbers
1, 2, 3, 4, and 5.
Skill 7
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 7
Practice on Your Own
List the first five multiples of 5.
Think: A multiple is the product
of the number and any whole
number except zero.
5
,
10
↑
1�5
,
↑
2�5
,
15
,
20
↑
3�5
25
↑
4�5
↑
5�5
The first five multiples of 5 are:
5, 10, 15, 20, 25.
List the first five multiples of the number.
2
8
,
,
,
,
↑
↑
↑
↑
↑
1 � 10 2 � 10 3 � 10 4 � 10 5 � 10
The first five multiples of 10 are:
,
,
,
,
↑
↑
↑
↑
↑
1�8 2�8
3�8
4�8
5�8
The first five multiples of 8 are:
3
4
11
The first five multiples of 11 are:
11,
,
,
20
20,
12,
,
,
,
,
� � 12 � � 12 � � 12 � � 12 � � 12
6
,
12
The first five multiples of 12 are:
,
� � 11 � � 11 � � 11 � � 11 � � 11
5
10
,
30
30,
,
,
,
List the next three multiples of the number.
7
4
4, 8, 12, 16, 20, 24,
8
,
,
7
7, 14, 21, 28, 35,
,
,
Check
List the next three multiples of the number.
9
15
15, 30, 45,
10
,
,
40
25
25, 50, 75,
,
,
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
Factors are two or more
numbers that are multiplied.
43
A factor always divides the
product without a remainder.
1
�
�6
�
�6
The factors of 6 are:
6
Find the whole-number factors.
Try These
↑
factors
1 � 8 � 8 ← product
Step 1 Use multiplication or
division facts to find factors.
Start with 1 � 8.
Every counting number has at
least two factors, 1 and the
number itself.
So, 1 and 8 are factors of 8.
Find all of the whole-number factors of 8.
Factors
2
� 10
�
� 10
The factors of 10 are:
�
2 and 4 are factors.
2�4�8
10
1 and 8 are factors.
1�8�8
Step 2 Test other factor pairs.
The only possible wholenumber factors of 8 are
numbers from 1 to 8.
Is 2 a factor?
© Houghton Mifflin Harcourt Publishing Company
2 and 4 are factors.
3 is not a factor, because
8 � 3 has a remainder.
When the factors repeat,
you have found all the
factors.
2�4�8
3�?�8
4�2�
3
�
�
� 16
� 16
Go to the next side.
�
� 16
The factors of 16 are:
16
So, the factors of 8 are 1, 2, 4,
and 8.
1 and 8 are factors.
1�8�8
Step 3 Continue until the
factors repeat.
Skill 8
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 8
Practice on Your Own
List all of the factors
of 7.
Think: Start
with 1 and 7. Then try
2, then 3, then 4, and
so on. If you repeat a
pair of factors, you
have found all
the factors.
1 � 7 � 7 ← 1 and 7 are factors.
2 � ? � 7 ← 2 is not a factor.
3 � ? � 7 ← 3 is not a factor.
4 � ? � 7 ← 4 is not a factor.
5 � ? � 7 ← 5 is not a factor.
6 � ? � 7 ← 6 is not a factor.
2, 3, 4, 5, and
6 are not factors
because when 7 is
divided by each of
these numbers, there
is a remainder.
7 � 1 � 7 ← These repeat.
You have found all the
factors.
The factors of 7 are 1
and 7.
Write all the factors of the number.
2
9
�
�9
�9
�
�
� 12
� 12
8
� 15
� 15
The factors of 17 are:
11
�
� 11
The factors of 11 are:
9
24
� 20
� 20
�
� 20
The factors of 20 are:
�
The factors of 15 are:
�
The factors of 12 are:
17
�
6
15
�
� 12
7
�
�
The factors of 14 are:
5
12
20
� 14
� 14
�
�
The factors of 9 are:
4
3
14
The factors of 24 are:
39
The factors of 39 are:
Check
Write all the factors of the numbers.
10
18
The factors of 18 are:
11
12
28
The factors of 28 are:
44
13
The factors of 13 are:
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
6
207
1
�
�
8 � 12
8 � 12 � (8 � 10) � (8 � 2)
↓
↓
2
�
�
7 � 15
7 � 15 � (7 � 10) � (7 � 5)
↓
↓
17
Step 1
Use grid paper.
Draw an array that shows
6 � 17.
Multiply.
Add.
3
�
�
Go to the next side.
5 � 19
5 � 19 � (5 � 10) � (5 � 9)
↓
↓
So, 6 � 17 � (6 � 10) � (6 � 7) � 102.
102
60 � 42
(6 � 10) � (6 � 7)
6
6 � (10 � 7) � (6 � 10) � (6 � 7)
7
10
Step 2
Break apart the grid to show the
factor 17 as the addends 10 � 7.
Skill 49
↓ ↓
Use the Distributive Property to find the products.
Try These
a � (b � c) � (a � b) � (a � c)
The Distributive Property of
Multiplication
Multiplying a sum by a number
is the same as multiplying each
addend by the number and then
adding the products.
Use the distributive property to find 6 � 17.
Multiplication Properties (Distributive)
© Houghton Mifflin Harcourt Publishing Company
Name
Skill
Holt McDougal Mathematics
Name
Skill
Skill 49
Practice on Your Own
Use the Distributive Property. Find 5 � 23.
1.
2.
3.
4.
Draw a 5 by 23 grid.
Break apart 23 as 20 and 3.
Find 5 � 20 and 5 � 3.
Add the products.
5 � 23 � (5 � 20) � (5 � 3)
↓
↓
� 100
�
15
� 115
Use the Distributive Property to find the product.
2
4 � 16
4 � 16 � (4 �
�
) � (4 �
)
6 � 22
6 � 22 � (6 �
�
�
�
3
) � (6 �
)
�
�
4
5 � 15
5 � 21
5 � 15 � (
�
)
5 � 21 � (
�
)
�(
�
)
�(
�
)
�
�
�
�
�
�
Check
Use the Distributive Property to find the product.
5
6
8 � 16
7 � 24
8 � 16 � (
�
)
7 � 24 � (
�
)
�(
�
)
�(
�
)
�
�
�
�
�
�
208
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
1
S
K
8
I
L
430
10. 100, 125, 150
9. 60, 75, 90
CHECK
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
12. 1, 13
11. 1, 2, 4, 7, 14, 28
10. 1, 2, 3, 6, 9, 18
CHECK
9. 1, 3, 13, 39
12, 24
8. 1, 2, 3, 4, 6, 8,
7. 1, 17
6. 1 � 11, 1, 11
3, 5, 15
5. 1 � 15, 3 � 5, 1,
6, 12
4. 1 � 12, 2 � 6,
10, 20
4 � 5, 1, 2, 4, 5,
3. 1 � 20, 2 � 10,
2, 7, 14
2. 1 � 14, 2 � 7, 1,
3, 9
1. 1 � 9, 3 � 3, 1,
PRACTICE
16
I
L
TRY THESE
10
K
3. 2, yes, 3, yes, 1,
composite
yes, 5, yes,
yes, 1, 17, not
5. 2, no, not prime
12. not prime
11. prime
10. not prime
CHECK
9. not prime
8. prime
7. not prime
composite
10. 1, 63, 3,
composite
9. 1, 29, not
composite
8. 1, 34, 2,
CHECK
composite
7. 1, 5, 45,
composite
6. 1, 28, 2,
not composite
5. 1, 37,
21, 3, composite
4. 2, yes, 3, no, 1,
composite
3. 2, yes, 3, yes, 4,
4. 2, no, not prime
6. 2, yes, prime
27, 3, composite
3. 2, no, not prime
2. 2, yes, 3, no, 1,
2. 2, yes, 3, yes, 4,
prime
PRACTICE
1. 2, no, 1, 52, 2,
1. 2, no, not prime
7, no
2. 2, no, 2, 5, yes
3. yes, yes, prime
yes
1. yes, 3, no, 3, 5,
S
2. no, not prime
prime
� 4, 1, 2, 4, 8,
6. 60, 90, 120, 150
8. 42, 49, 56
L
PRACTICE
3 � 4, 1, 2, 3, 4,
7. 28, 32, 36
9
I
TRY THESE
K
1. yes, 3, yes,
S
3. 1 � 16, 2 � 8, 4
2, 5, 10
2. 1 � 10, 2 � 5, 1,
2, 3, 6
5. 40, 60, 80, 100
1, 2, 3, 4, 5
4. 24, 36, 48, 60,
1, 2, 3, 4, 5
3. 22, 33, 44, 55,
40, 50
50; 10, 20, 30,
2. 10, 20, 30, 40,
8, 16, 24, 32, 40
1. 8, 16, 24, 32, 40;
PRACTICE
6, 12, 18, 24, 30
3. 6, 12, 18, 24, 30;
4, 6, 8, 10
2. 2, 4, 6, 8, 10; 2,
6, 9, 12, 15
1. 1 � 6, 2 � 3, 1,
L
1. 3, 6, 9, 12, 15; 3,
7
L
L
TRY THESE
S
I
L
TRY THESE
K
L
Answers
L
L
TRY THESE
48
I
CHECK
Property
I
L
TRY THESE
49
K
442
Property
� 105
� 100 + 5
(5 � 20) � (5 � 1)
4. 5 � 21 �
Property
10. 4; Commutative
� 75
© Houghton Mifflin Harcourt Publishing Company
(5 � 10) � (5 � 5)
� 50 � 25
9. 2; Associative
Property
8. 5; Associative
3. 5 � 15 �
answer given.
7. 32; Commutative
Property
may vary. Sample
In Ex. 3–6, factors
� 132
� 120 � 12
(6 � 20) � (6 � 2)
2. 6 � 22 �
� 64
� 40 � 24
(4 � 10) � (4 � 6)
1. 4 � 16 �
PRACTICE
3. 50 � 45; 95
2. 70 � 35; 105
1. 80 � 16; 96
S
6. 1; Property of One
Zero
5. 0; Property of
Property
4. Associative
3. Property of One
One
Property
2. Property of Zero
Property
14. 52; Property of
1. Commutative
13. 15; Commutative
12. 5; Associative
4. 0
Zero
11. 0; Property of
S
3. 1
PRACTICE
L
L
2. 2 � (8 � 5)
I
48
K
L
1. 6 � 7
S
K
I
L
S
� 168
� 140 � 28
(7 � 20) � (7 � 4)
6. 7 � 24 �
� 128
� 80 + 48
(8 � 10) � (8 � 6)
5. 8 � 16 =
CHECK
49
K
L
Holt McDougal Mathematics
Answers