Deck 5: Number Theory and the Real Number System

Question 1

Determine whether or not the first number is divisible by the second number
125,992; 9

A) No
B) Yes

Answer 1

A

Question 2

Find the prime factorization of the number
468

Answer 2

A

Question 3

Determine whether or not the first number is divisible by the second number
22,669; 6

A) No
B) Yes

Answer 3

A

Question 4

Determine whether or not the first number is divisible by the second number
42,020; 4

A) Yes
B) No

Question 5

Determine whether or not the first number is divisible by the second number
47,490; 10

A) Yes
B) No

Question 6

Find the prime factorization of the number
45

A)5
B)9 ∙ 3
C)52
D) 9 ∙ 5

Question 7

Determine whether or not the first number is divisible by the second number
27,140; 8

A) Yes
B) No

Question 8

Determine whether or not the first number is divisible by the second number
1978; 2

A) Yes
B) No

Question 9

Find the prime factorization of the number
90

Question 10

Determine whether or not the first number is divisible by the second number
12,803; 3

A) Yes
B) No

Question 11

Find the prime factorization of the number
7425

Question 12

Determine whether or not the first number is divisible by the second number
521,364; 3

A) Yes
B) No

Question 13

Find the prime factorization of the number
231

Question 14

Determine whether or not the first number is divisible by the second number
398,763; 9

A) No
B) Yes

Question 15

Determine whether or not the first number is divisible by the second number
394,091; 4

A) Yes
B) No

Question 16

Determine whether or not the first number is divisible by the second number
652,523; 5

A) Yes
B) No

Question 17

Determine whether or not the first number is divisible by the second number
955,575; 5

A) Yes
B) No

Question 18

Determine whether or not the first number is divisible by the second number
22,308; 6

A) No
B) Yes

Question 19

Determine whether or not the first number is divisible by the second number
22,259; 2

A) No
B) Yes

Question 20

Determine whether or not the first number is divisible by the second number
15,416; 8

A) Yes
B) No

Question 21

Find the least common multiple (LCM).
At Lincoln High School, there are 1472 students in the Junior Class and 2576 students in the Senior
Class. The teachers want to assign the students to committees with the same number of juniors in
Each committee and the same number of seniors in each committee. (For example, there might be 2
Juniors and 3 seniors in every committee). What are all the possible numbers of committees they
Could form and still meet this goal?

A) 4, 16, 92, 368, or 644 different committees
B) 4, 23, 64, or 368 different committees
C) 4, 23, 16, 92, or 368 different committees
D) 4, 23, 16, or 64 different committees

Question 22

Find the prime factorization of the number
62

Question 23

Find the least common multiple (LCM).
120 and 90

A) 30
B) 720
C) 1080
D) 360

Question 24

Find the least common multiple (LCM).
Janine and Thor are both running for class president. Janine goes down a hallway in the school
And puts a sticker on every fourth locker. Thor goes down the same hallway, putting one of his
Stickers on every fifth locker. If there are 130 lockers in the hallway, how many have both studentsʹ
Stickers?

A) 20
B) 13
C) 6
D) 26

Question 25

Find the least common multiple (LCM).
Several different bus routes stop at the corner of Second St. and Lincoln Ave. A Wilkenson bus
Arrives every 18 minutes, a Fifth Avenue bus arrives every 45 minutes and a Harris Road bus
Arrives every 10 minutes. If both buses arrive at the stop at 5:07 AM, how many minutes will pass
Before both buses arrive at the same time again?

A) 10 minutes
B) 90 minutes
C) 45 minutes
D) 8100 minutes

Question 26

Find the greatest common divisor (GCD).
14, 18, and 20

A) 1
B) 14
C) 4
D) 2

Question 27

Find the prime factorization of the number
32,625

Question 28

Find the greatest common divisor (GCD).
42, 56, and 98

A) 7
B) 1
C) 14
D) 42

Question 29

Find the least common multiple (LCM).
Several different bus routes stop at the corner of Second St. and Lincoln Ave. A Wilkenson bus
Arrives every 27 minutes and a Harris Road bus arrives every 15 minutes. If both buses arrive at
The stop at 5:07 AM, when will they again arrive at the same time?

A) 6:42 AM
B) 7:22 AM
C) 11:52 AM
D) 9:12 AM

Question 30

Find the least common multiple (LCM).
48, 162, and 9

A) 1296
B) 432
C) 324
D) 648

Question 31

Find the least common multiple (LCM).
56 and 96

A) 1344
B) 672
C) 168
D) 224

Question 32

Find the least common multiple (LCM).
45, 28, and 150

A) 1,050
B) 630
C) 1260
D) 6300

Question 33

Find the greatest common divisor (GCD).
120 and 270

A) 30
B) 6
C) 10
D) 15

Question 34

Find the least common multiple (LCM).
At Northwest High School, there are 1472 students in the Junior Class and 1012 students in the
Senior Class. To let the juniors work with more experienced students, the teachers want to assign
The students to committees with the same number of juniors in each committee and the same
Number of seniors in each committee. (For example, there might be 2 juniors and 3 seniors in every
Committee). What is the largest number of committees that can be formed?

A) 23 committees
B) 368 committees
C) 4 committees
D) 92 committees

Question 35

Find the least common multiple (LCM).
At Northwest High School, there are 207 students in the Sophomore Class, 243 students in the
Junior Class, and 216 students in the Senior Class. The teachers want to assign the students to
Committees with the same number of sophomores, juniors, and seniors in each committee. (For
Example, there might be 4 sophomores, 2 juniors, and 3 seniors in every committee). What is the
Largest number of committees that can be formed?

A) 72
B) 3
C) 27
D) 9

Question 36

Find the greatest common divisor (GCD).
8 and 12

A) 4
B) 2
C) 1
D) 8

Question 37

Find the greatest common divisor (GCD).
30 and 19

A) 19
B) 3
C) 10
D) 1

Question 38

Find the least common multiple (LCM).
60, 80, and 50

A) 240
B) 600
C) 400
D) 1200

Question 39

Find the greatest common divisor (GCD).
30 and 36

A) 6
B) 1
C) 3
D) 2

Question 40

Find the prime factorization of the number
1162

Question 41

Evaluate the expression.
-17 + 14 + (-1)

A) -2
B)32
C)-4
D)30

Question 42

Provide an appropriate response.
True or False? 3 is a factor of 6.

Question 43

Provide an appropriate response.
True or False? If a number is divisible by 2, then every digit of the number is divisible by 2.

Question 44

Provide an appropriate response.
True or False? If a number is not divisible by 10, then it is not divisible by 20.

Question 45

Provide an appropriate response.
True or False? 2|6

Question 46

Evaluate the expression.
-23 + 9

A) 14
B) -32
C) 32
D) -14

Question 47

Provide an appropriate response.
Choose the number that is divisible by 2, 3, 7, 6, and 14.

A) 114
B) 142
C) 42
D) 21

Question 48

Provide an appropriate response.
True or False? 10|2

Question 49

Evaluate the expression.
1 + (-25) + (-15)

A) -39
B) 11
C) 41
D) -9

Question 50

Evaluate the expression.
-60 + 61

A) -1B)-121
C) 121
D) 1

Question 51

Provide an appropriate response.
True or False? 15 is divisible by 3.

Question 52

Evaluate the expression.
-10 + (-21)

A) 11
B) -31
C) 31
D) -11

Question 53

Evaluate the expression.
-17 + (-50) + 70 + (-60)

A) -23
B) 63
C) -197
D) -57

Question 54

Evaluate the expression.
9 + (-13)

A) -22
B) 22
C) -4D)4

Question 55

Evaluate the expression.
11 + 23 + (-12)

A) -24
B) 46
C) 0
D) 22

Question 56

Provide an appropriate response.
True or False? If a number is divisible by 3, then the number must also be divisible by 6.

Question 57

Provide an appropriate response.
True or False? 6 is a multiple of 3.

Question 58

Provide an appropriate response.
True or False? 3 is a multiple of 15.

Question 59

Provide an appropriate response.
True or False? If a number is divisible by 7 and 3, then the number is divisible by 21.

Question 60

Provide an appropriate response.
True or False? 3 is divisible by 6.

Question 61

Evaluate the expression.
-7 - (-3)

A) 10
B) 4
C) -4D)-10

Question 62

Evaluate the expression.

Question 63

Evaluate the expression.
15 - (-10)

A) 5
B) -5C)-25
D) 25

Question 64

Evaluate the expression.
[4 + (-4)] + (-5 + 8)

A) 3
B) -13
C) 21
D) 13

Question 65

Evaluate the expression.
(-3)(9)(-5)

A) -17
B) -135
C) 135
D) 17

Question 66

Evaluate the expression.
(-16)(-9)

A) -144
B) -7
C) 144
D) 7

Question 67

Evaluate the expression.
(-4)(-4)(-8)

A) -128
B) -28
C) 128
D) -138

Question 68

Evaluate the expression.
-5 ∙ 3

A) -2B) 2C)15
D) -15

Question 69

Evaluate the expression.
(-16 + 17) + (-3 + 10)

A) 8
B) 14
C) -26
D) 40

Question 70

Evaluate the expression.
(-9)(-9)(-9)

A) -739
B) -729
C) 729
D) -719

Question 71

Evaluate the expression.
(-3)(-6)

A) -9B)-18
C) 9D) 18

Question 72

Evaluate the expression.
(-5)(-3)(6)

A) 80
B) 190
C) 90
D) -90

Question 73

Evaluate the expression.
9 - 14

A) -5
B) 5
C) 23
D) -23

Question 74

Evaluate the expression.
(-3)(-3)

A) -19
B) 19
C) -9D)9

Question 75

Evaluate the expression.
[(-3)(-3)] ∙ [7(-5)]

A) 315
B) 45
C) -45
D) -315

Question 76

Evaluate the expression.
(-6)(-8)(-8)

A) 384
B) -374
C) 96
D) -384

Question 77

Evaluate the expression.
(15 + 11) - (13 - 15)

A) 28
B) 32
C) 2
D) -32

Question 78

Evaluate the expression.
(-6 - 1) - (-14 + 11)

A) -32
B) -2C)10D)-4

Question 79

Evaluate the expression.
11 - (12 - 20)

A) 19
B) 3
C) -21
D) 43

Question 80

Evaluate the expression.
-5 - 10

A) 5
B) -15
C) -5D)15