Deck 4: Number Theory

Question 1

If a number is divisible by 3 and 5, then it must also be divisible by 15.

Answer 1

True

Question 2

Is 233,682 divisible by 3?

A)Yes
B)No

Answer 2

A

Question 3

Is 198,819 divisible by 9?

A)Yes
B)No

Answer 3

A

Question 4

Is 839,254 divisible by 9?

A)Yes
B)No

Question 5

Is 210,270 divisible by 30?

A)Yes
B)No

Question 6

Is 34,210 divisible by 10?

A)Yes
B)No

Question 7

If a number is divisible by 8, then it is also divisible by 16.

Question 8

Is 62,656,837 divisible by 77?

A)Yes
B)No

Question 9

Is 18,871 divisible by 6?

A)Yes
B)No

Question 10

Is 6,703,279 divisible by 11?

A)Yes
B)No

Question 11

If a number is divisible by 5, then every digit of the number is divisible by 5.

Question 12

Is 22,233 divisible by 2?

A)Yes
B)No

Question 13

Is 732,275 divisible by 5?

A)Yes
B)No

Question 14

If a number is divisible by 2, then it must also be divisible by 6.

Question 15

Is 952,042 divisible by 4?

A)Yes
B)No

Question 16

Is 927,441 divisible by 5?

A)Yes
B)No

Question 17

Is 23,868 divisible by 6?

A)Yes
B)No

Question 18

Is 203 divisible by 3?

A)Yes
B)No

Question 19

Is 67,072 divisible by 4?

A)Yes
B)No

Question 20

Is 85,104,901 divisible by 11?

A)Yes
B)No

Question 21

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 22

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 23

Question 24

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 25

Question 26

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 27

Question 28

Question 29

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 30

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 31

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 32

Question 33

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 34

Question 35

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 36

Question 37

Question 38

Question 39

Question 40

Classify as true or false, assuming that a, b, c, and d are whole numbers an

Question 41

What is the greatest prime number you must consider to test whether 3599 is prime?

A)59
B)63
C)64
D)31

Question 42

Find the prime factorization.

Question 43

The local bakery marked down some day-old pies from $4.00 but kept the price over $3.00. All of the pies were sold, and the total amount of money from the sale of the pies was $43.55. How many
Pies were sold?

A)13
B)12
C)15
D)14

Question 44

In a football game a touchdown is worth 6 points, an extra point is worth 1 point, and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns, extra
Points and field goals. If a team scored 56 points with 7 touchdowns and 2 extra points, how many
Field goals were scored?

A)4
B)3
C)5
D)7

Question 45

Reuben is planting a large garden filled with corn. Can he plant 136 corn plants in 8 equal rows?

A)Yes
B)No

Question 46

Find the prime factorization.

Question 47

Find the least number divisible by each natural number less than or equal to 10.

A)30,240
B)3,628,800
C)2520
D)100

Question 48

Jason bought a new bike for $678, and he plans to make equal monthly payments to pay for it. Can he pay off the bike in 3 equal payments?

A)Yes
B)No

Question 49

How many twin prime pairs can be found from the numbers less than 100?

A)9
B)8
C)10
D)7

Question 50

Find the least positive number divisible by two primes.

A)4
B)2
C)3
D)6

Question 51

Find the greatest 3-digit number that has exactly three factors.

A)973
B)999
C)961
D)963

Question 52

In a football game a touchdown is worth 6 points, an extra point is worth 1 point, and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns, extra
Points and field goals. If a team scored 66 points with 6 touchdowns and 6 extra points, how many
Field goals were scored?

A)6
B)8
C)9
D)7

Question 53

List all digits that cannot appear in a superprime number.

A)4, 6, 8, 0
B)4, 6, 8
C)4, 6, 8, 5
D)4, 6, 8, 0, 5

Question 54

There is a number that has 2, 5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?

A)80
B)40
C)320
D)70

Question 55

A group of teachers order markers for their classrooms. The bill was $3.91. If the original price per marker was 17¢ and the price has risen, how much does each marker cost now?

A)23¢
B)24¢
C)22¢
D)21¢

Question 56

Find the prime factorization.

Question 57

Find the prime factorization.

Question 58

Find the largest two-digit superprime.

A)79
B)97
C)59
D)95

Question 59

Aryana is organizing the seating for a banquet. Is it possible for her to sit 289 people at 12 different tables so that each table has the same number of people?

A)Yes
B)No

Question 60

Question 61

If all of 48 available apple trees are to be planted in a rectangular array, what are the possible numbers of rows in the array, all rows having the same number of trees?

A)1, 2, 3, 4, and 6
B)8, 12, 16, 24, and 48
C)1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
D)1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, and 48

Question 62

If all of 82 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many
Different arrays are there?

A)No
B)Yes, two.
C)Yes, three.

Question 63

If all of 47 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many
Different arrays are there?

A)Yes
B)No

Question 64

If a group of 247 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible group sizes?

A)19
B)9 and 13
C)13 and 19
D)7, 13, and 19

Question 65

If a bag of jellybeans has 105 jellybeans, what is the greatest number of bowls that can be filled with 35 jellybeans?

A)35
B)3
C)25
D)8

Question 66

Question 67

If a group of 238 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible numbers of groups?

A)14, 17, 34, and 119
B)2, 7, 14, 17, 34, and 119
C)2, 7, 14, and 17
D)14 and 17

Question 68

Find the GCD or LCM as indicated.
Given 208 and 135, find the GCD.

A)65
B)1
C)6
D)104

Question 69

If a group of 284 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible group sizes?

A)2, 3, and 4
B)2 and 28
C)3 and 4
D)2 and 4

Question 70

Find the GCD or LCM as indicated.
Given 48, 162, and 9, find the LCM.

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

Question 71

Find the GCD or LCM as indicated.
Given 8 and 28, find the LCM.

A)28
B)224
C)14
D)56

Question 72

Question 73

Find the GCD or LCM as indicated.
Given 240 and 13,500, find the GCD.

A)60
B)240
C)180
D)30

Question 74

Find the GCD or LCM as indicated.
Given 30 and 90, find the LCM.

A)90
B)270
C)180
D)30

Question 75

Find the largest three-digit superprime.

A)597
B)799
C)797
D)999

Question 76

Find the GCD or LCM as indicated.
Given 240, 10,000, and 2250, find the GCD.

A)20
B)30
C)50
D)10

Question 77

Find the GCD or LCM as indicated.
Given 56 and 96, find the LCM.

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

Question 78

Find the GCD or LCM as indicated.
Given 60 and 30, find the GCD.

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

Question 79

Jim has 56 trees that he wants to plant in a rectangular array. List the possible arrays.

Question 80

Find the GCD or LCM as indicated.