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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.


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) 3 x 4 x 5 x 6 x 7

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


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


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.


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


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


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


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?


77) A radio station is giving away prizes to its callers. Depending on what number

caller you are, you receive a different prize.

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.

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?

Prizes Caller

Hat Every 3rd caller

T-shirt Every 5th caller

Backpack Every 6th caller

Items Bags

Hat Every 2nd visitor

T-shirt Every 7th visitor

Backpack Every 10th visitor


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? ______


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?


Answer Key

1) Odd

2) Odd

3) Even

4) Even

5) Odd

6) Even

7) Even

8) Even

9) Even

10) Even

11) Even

12) Even

13) Even

14) Even

15) Even

16) Even

17) Odd

18) Odd

19) Odd

20) Even

21)

2 3 4 5 8 9 10

480

204

475

596

2,205

20,043

211,032

4,128,796

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)

2 3 4 5 8 9 10

396

456

848

720

4,132


13,156

362,880

4,031,037

28) 15, 54, 51, 57, 102

29) 63, 108, 261, 432, 216, 639

30) 3 x 7,023

31) 9 x 512

32) The sum of the digits is 9 and it is

divisible by both 3 and 9.

33) 8

34) 1

35) 7

36) 15

37) 3

38) 6

39) 3

40) 2

41) 9

42) 3

43) 15

44) 10

45) 2

46) 3

47) 7

48) 9

49) 9

50) 1

51) 3

52) 9

53) 63

54) 240

55) 30

56) 84

57) 180

58) 40

59) 18

60) 30

61) 56

62) 110

63) 45

64) 28

65) 60

66) 90

67) 56

68) 143

69) 42

70) 12

71) 126

72) 88

73) a. 6 containers b. 5 oatmeal and 8 chocolate

chip

74) Every 40 minutes 75)

a. 18 key chains b. 5 blue, 4 yellow

76)

a. 9 bouquets b. 4 roses, 3 tulips, 2

carnations 77) 30th caller


78) 5 times 79)

a. 8 arrangements b. 4 maroon, 3 white, 2

orange

80) 70th visitor 81) 16 rows 82) 6 packages of red, 5 packages of

yellow

Fraction and Decimal Computations Unit Review

Multiple Choice Questions Answer Key

83) b

84) d

85) c

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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