Factors and Multiples Chapter Questions
1. What is the divisibility rule for 3?
2. What is the divisibility rule for 9?
3. Explain LCM.
4. Explain GCF.
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Chapter Problems
Even and Odd Numbers
Classwork
Determine whether each sum or product will be even or odd. Explain your reasoning.
1)
42,506 + 17,243
2)
983 x 455
3)
6,729 + 15,227
4)
54,294 x 31,871
5)
1,691 + 784
6)
7,330 x 318
7)
81,348 + 97,316
8)
2,773 x 6,228
9)
10 + 11 + 12 + 13 + 14
10)
3x4x5x6x7
Homework
Determine whether each sum or product will be even or odd. Explain your reasoning.
11)
72,347 + 90,101
12)
458 x 836
13)
3,770 + 5,422
14)
10,234 x 11,329
15)
568 + 678
16)
1,945 x 3,734
17)
8,779 + 5,338
18)
313 x 797
19)
13 + 14 + 15 + 16 + 17
20)
8 x 9 x 10 x 11 x 12
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Divisibility Rules for 3 & 9
Classwork
21)
If the number to the left of each row is divisible by the number at the top of the
column, put a check mark in the box.
2
3
4
5
8
9
10
480
204
475
596
2,205
20,043
211,032
4,128,796
22)
Which of the following numbers are divisible by 3? Explain.
94, 36, 64, 21, 91, 48, 74, 28, 75, 19
23)
Which of the following numbers are divisible by 9? Explain.
72, 66, 45, 144, 171, 234, 245, 559, 612, 718
24)
Is 4,314 divisible by 3? If it is, write the number as the product of 3 and another
factor. If not, explain.
25)
Is 2,376 divisible by 9? If it is, write the number as the product of 9 and another
factor. If not, explain.
26)
Explain why 5,868 is divisible by both 3 and 9.
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Homework
27)
If the number to the left of each row is divisible by the number at the top of the
column, put a check mark in the box.
2
3
4
5
8
9
10
396
456
848
720
4,132
13,156
362,880
4,031,037
28)
Which of the following numbers are divisible by 3? Explain.
15, 54, 43, 51, 91, 57, 76, 23, 35, 102
29)
Which of the following numbers are divisible by 9? Explain.
63, 89, 108, 261, 139, 432, 216, 639, 910, 1023
30)
Is 21,069 divisible by 3? If it is, write the number as the product of 3 and
another factor. If not, explain.
31)
Is 4,608 divisible by 9? If it is, write the number as the product of 9 and another
factor. If not, explain.
32)
Explain why 3,042 is divisible by both 3 and 9.
Greatest Common Factor
Classwork
Find the Greatest Common Factor of each set of numbers.
33) 72 and 64
34)
15 and 16
35)
14 and 49
36)
15 and 75
37)
66 and 147
38)
78 and 42
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39)
75 and 18
40)
98 and 66
41)
27 and 72
42)
18 and 21
Homework
Find the Greatest Common Factor of each set of numbers.
43) 30 and 45
44)
70 and 130
45)
98 and 30
46)
45 and 66
47)
77 and 21
48)
63 and 45
49)
36 and 63
50)
21 and 40
51)
6 and 51
52)
63 and 99
Least Common Multiple
Classwork
Find the Least Common Multiple of each set of numbers.
53) 9 and 21
54)
12 and 80
55)
6 and 10
56)
14 and 12
57)
15 and 36
58)
8 and 20
59)
9 and 6
60)
15 and 10
61)
8 and 14
62)
55 and 22
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Homework
Find the Least Common Multiple of each set of numbers.
63) 9 and 15
64)
4 and 7
65)
12 and 15
66)
10 and 9
67)
8 and 14
68)
11 and 13
69)
42 and 21
70)
4 and 6
71)
14 and 63
72)
22 and 8
GCF/LCM Applications
Classwork
73) Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in
plastic containers for her friends at school. She wants to divide the cookies into
identical containers so that each container has the same number of each kind
of cookie.
a. If she wants each container to have the greatest number of cookies
possible, how many plastic containers does she need?
b. How many of each cookie will she put in each container?
74)
Beginning at 8:30 A.M., tours of the National Capitol and the White House begin
at a tour agency. Tours for the National Capitol leave every 8 minutes. Tours for
the White House leave every 10 minutes. How often do the tours leave at the
same time?
75)
Joe is making key chains with beads. He wants each key chain to have the
same number of beads. He has 90 blue beads and 72 yellow beads.
a. What is the greatest number of key chains he can make that are exactly
the same?
b. How many of each color bead will be on each key chain?
76)
A florist has 36 roses, 27 tulips, and 18 carnations she must use to create
bouquets.
a. What is the largest number of bouquets she can make without having any
flowers left over?
b. How many of each flower will she put in each bouquet?
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77)
A radio station is giving away prizes to its callers. Depending on what number
caller you are, you receive a different prize.
Prizes
Caller
Hat
Every 3rd caller
T-shirt
Every 5th caller
Backpack Every 6th caller
What number caller will be the first to receive all 3 prizes?
Homework
78)
Two neon lights are turned on at the same time. One blinks every 4 seconds
and the other blinks every 6 seconds. In 60 seconds, how many times will they
blink at the same time?
79)
Shannon is making identical balloon arrangements for a party. She has 32
maroon balloons, 24 white balloons, and 16 orange balloons. She wants each
arrangement to have the same number of each color.
a. What is the greatest number of arrangements that she can make if every
balloon is used?
b. How many balloons of each color will be in each arrangement?
80)
At a display booth at an amusement park, every visitor gets a gift bag. Some of
the bags have items in them as shown in this table.
Items
Bags
Hat
Every 2nd visitor
T-shirt
Every 7th visitor
Backpack Every 10th visitor
What number visitor will be the first to receive all 3 items in the gift bag?
81)
There are 48 girls and 64 boys in the school choir. The choir teacher plans to
arrange the students in equal rows. The same number of boys and the same
number of girls will be in each row. What is the greatest number of rows the
teacher can arrange?
82)
Mike can buy red push pins in packages of 10 and yellow push pins in
packages of 12. What is the least amount of packages of each color he must
buy in order to have the same number of pins?
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Factors and Multiples Chapter Review
Multiple Choice Questions
83)
Find the Greatest Common Factor of 24 and 72.
a. 12
b. 24
c. 6
d. 72
84)
What is the Least Common Multiple of 3 and 18?
a. 36
b. 6
c. 3
d. 18
85)
4 is the GCF of which two numbers?
a. 8 and 16
b. 16 and 32
c. 8 and 12
d. 24 and 36
86)
48 is the LCM of which two numbers?
a. 16 and 48
b. 12 and 4
c. 6 and 8
d. 2 and 24
87)
Which of the following numbers is divisible by both 3 and 9?
a. 15
b. 89
c. 102
d. 234
Short Constructed Response Questions
88)
What is the GCF of 15 and 54? ______
89)
What is the LCM of 16 and 36? ______
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Extended Constructed Response Questions
90)
Miriam’s uncle donated 120 cans of juice and 90 packs of cheese crackers for
the school field trip. Each student is to receive the same number of cans of juice
and the same number of packs of crackers.
a. What is the greatest number of students that can go on the field trip and
share the food equally with no food left over?
b. How many cans of juice and how many packs of crackers will each student
receive? Explain.
91)
Jeremy and his little sister, Deborah, are at a carnival. There are both a large
and a small Ferris wheel. Jeremy gets on the large Ferris wheel at the same
time his sister gets on the small Ferris wheel. The rides begin at the same time.
The large wheel makes one revolution in 10 seconds and the small wheel
makes one revolution in 7 seconds.
a. How many seconds will pass before Jeremy and Deborah are at the bottom at
the same time again?
b. How many times will each Ferris wheel go around before Jeremy and his sister
are both on the ground again?
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Answer Key
1)
Odd
11) Even
2)
Odd
12) Even
3)
Even
13) Even
4)
Even
14) Even
5)
Odd
15) Even
6)
Even
16) Even
7)
Even
17) Odd
8)
Even
18) Odd
9)
Even
19) Odd
10) Even
20) Even
21)
480
204
475
596
2,205
20,043
211,032
4,128,796
2
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3
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4
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5
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8
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9
10
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22) 36, 21, 48, 75
23) 72, 45, 144, 171, 234, 612
24) 3 x 1,438
25) 9 x 264
26) The sum of the digits is 27 and it is divisible by both 3 and 9.
27)
396
456
848
720
4,132
2
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

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5
8
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9
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10
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13,156
362,880
4,031,037
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28) 15, 54, 51, 57, 102
55) 30
29) 63, 108, 261, 432, 216, 639
56) 84
30) 3 x 7,023
57) 180
31) 9 x 512
58) 40
32) The sum of the digits is 9 and it is
59) 18
divisible by both 3 and 9.

60) 30
33) 8
61) 56
34) 1
62) 110
35) 7
63) 45
36) 15
64) 28
37) 3
65) 60
38) 6
66) 90
39) 3
67) 56
40) 2
68) 143
41) 9
69) 42
42) 3
70) 12
43) 15
71) 126
44) 10
72) 88
45) 2
73)
a. 6 containers
b. 5 oatmeal and 8 chocolate
chip
46) 3
47) 7
48) 9
74) Every 40 minutes
75)
a. 18 key chains
b. 5 blue, 4 yellow
49) 9
50) 1
51) 3
76)
52) 9
a. 9 bouquets
b. 4 roses, 3 tulips, 2
carnations
77) 30th caller
53) 63
54) 240
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80) 70th visitor
81) 16 rows
82) 6 packages of red, 5 packages of
yellow
78) 5 times
79)
a. 8 arrangements
b. 4 maroon, 3 white, 2
orange
Fraction and Decimal Computations Unit Review
Multiple Choice Questions Answer Key
83) b
85) c
84) d
86) a
87) d
Short Constructed Response Questions Answer Key
88) 3
89) 144
Extended Constructed Response Questions Answer Key
90)
a. 30 students can go on the field trip.
b. Each student will get 4 cans of juice and 3 packs of crackers; 30 is the
GCF, so 4 x 30 = 120 (juice) and 3 x 30 = 90 (crackers)
91)
a. It will be 70 seconds before they are both on the bottom again.
b. The large Ferris Wheel will go around 7 times, small will go 10 times.
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