Deck 5: Number Theory

Question 1

Every composite number is divisible by 2.

Answer 1

False

Question 2

Use divisibility tests to decide whether the first number is divisible by the second.
615,849; 9

A)Yes
B)No

Answer 2

B

Question 3

Find all natural number factors of the number.
484

A)1, 2, 3, 4, 11, 22, 121, 242, 484
B)1, 2, 4, 11, 22, 44, 121, 242, 484
C)1, 2, 11, 121, 484
D)1, 2, 4, 11, 22, 33, 44, 121, 242, 484

Answer 3

B

Question 4

All prime numbers are odd.

Question 5

Find all natural number factors of the number.
47

A)1, 47
B)1, 2, 3, 15, 23, 47
C)1, 2, 4, 15, 23, 47
D)1, 2, 23, 47

Question 6

Use divisibility tests to decide whether the first number is divisible by the second.
938,772; 9

A)Yes
B)No

Question 7

Find all natural number factors of the number.
110

A)2, 5, 10, 11, 55, 110
B)1, 2, 5, 10, 11, 22, 110
C)1, 2, 5, 10, 11, 22, 55, 110
D)1, 2, 4, 5, 10, 11, 22, 55, 110

Question 8

If a number is divisible by both 3 and 9 then it is divisible by 27.

Question 9

If n is a natural number and 20|n, then 10|n.

Question 10

If a natural number is divisible by 2, then it must also be divisible by 10.

Question 11

Use divisibility tests to decide whether the first number is divisible by the second.
574,085; 4

A)Yes
B)No

Question 12

Find all natural number factors of the number.
42

A)1, 2, 3, 7, 6, 14, 21, 42
B)1, 2, 3, 7, 6, 14, 28, 42
C)1, 7, 42
D)7, 6, 14, 42

Question 13

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

Question 14

Use divisibility tests to decide whether the first number is divisible by the second.
6,955,200; 7 [Note that a divisibility test for 7 is as follows:
Double the last digit of the number and subtract this value from the original number with the last
Digit omitted. Repeat this process as many times as necessary until the number obtained can easily
Be divided by 7. If the final number obtained is divisible by 7, then so is the original number. If the
Final number obtained is not divisible by 7, then neither is the original number.]

A)Yes
B)No

Question 15

Use divisibility tests to decide whether the first number is divisible by the second.
467,661; 3

A)Yes
B)No

Question 16

Question 17

There are 35 prime numbers smaller than 150.

Question 18

A prime number may have one or two different natural number factors but may not have more
than two different natural number factors.

Question 19

Find all natural number factors of the number.
125

A)1, 5, 25
B)1, 5, 25, 125
C)5, 62, 125
D)5, 25, 125

Question 20

Use divisibility tests to decide whether the first number is divisible by the second.
404,036; 4

A)Yes
B)No

Question 21

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
533x is divisible by 11.

Question 22

Give the prime factorization of the number. Use exponents when possible.
4725

Question 23

Give the prime factorization of the number. Use exponents when possible.
177

Question 24

Give the prime factorization of the number. Use exponents when possible.
396

Question 25

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
74,3x2 is divisible by 6.

Question 26

Give the prime factorization of the number. Use exponents when possible.
154

Question 27

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
214,21x is divisible by 11.

Question 28

Use divisibility tests to decide whether the first number is divisible by the second.
322,695; 9

A)Yes
B)No

Question 29

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.

Question 30

Use divisibility tests to decide whether the first number is divisible by the second.
827,711; 5

A)Yes
B)No

Question 31

Use divisibility tests to decide whether the first number is divisible by the second.
139,243,105; 11 [Note that a divisibility test for 11 is as follows:
Starting at the left of the number, add together every other digit. Add together the remaining digits.
Subtract the smaller of the two sums from the larger. If the final number obtained is divisible by 11,
Then so is the original number. If the final number obtained is not divisible by 11, then neither is the
Original number.]

A)Yes
B)No

Question 32

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
43x2 is divisible by 9.

Question 33

Give the prime factorization of the number. Use exponents when possible.
2937

Question 34

414,3x2 is divisible by 8 but not 16.

Question 35

Use divisibility tests to decide whether the first number is divisible by the second.
348,951; 10

A)Yes
B)No

Question 36

Give the prime factorization of the number. Use exponents when possible.
28

Question 37

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
4x21 is divisible by 4.

Question 38

Give the prime factorization of the number. Use exponents when possible.
936

Question 39

Give the prime factorization of the number. Use exponents when possible.
198

Question 40

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
43x6 is divisible by 4.

Question 41

Every natural number of the form 4k + 5 is prime.

Question 42

Find the number of divisors of the number.
360

A)36
B)12
C)24
D)18

Question 43

Use the formula indicated to determine the prime number generated for the given value of n.

A)223
B)2797
C)141
D)197

Question 44

43x0 is divisible by 6.

Question 45

Use the formula indicated to determine the prime number generated for the given value of n.

A)1163
B)3801
C)2241
D)1149

Question 46

Use the formula indicated to determine the prime number generated for the given value of n.

A)2393
B)113
C)-809
D)971

Question 47

Find the number of divisors of the number.

Question 48

Determine whether the statement is true or false.

Question 49

Use the formula indicated to determine the prime number generated for the given value of n.

A)97
B)2297
C)15
D)113

Question 50

Determine whether the statement is true or false.

Question 51

417,30x is divisible by 8 but not 16.

Question 52

Determine whether the statement is true or false.

Question 53

Use the formula indicated to determine the prime number generated for the given value of n.

A)1395
B)771
C)797
D)853

Question 54

Find the number of divisors of the number.
400

A)16
B)8
C)12
D)15

Question 55

Find the number of divisors of the number.
54

A)12
B)6
C)9
D)8

Question 56

Use the formula indicated to determine the prime number generated for the given value of n.

A)7759
B)4201
C)10,961
D)691

Question 57

Determine whether the statement is true or false.

Question 58

Determine whether the statement is true or false.

Question 59

Find the number of divisors of the number.
60

A)14
B)12
C)16
D)10

Question 60

Every natural number of the form 4k + 4 is prime.

Question 61

All prime numbers are also deficient numbers.

Question 62

Determine whether the number is abundant or deficient.
108

A)Abundant
B)Deficient

Question 63

Determine whether the statement is true or false.
The proper divisors of a natural number include all divisors of the number except 1.

Question 64

All composite numbers are also abundant numbers.

Question 65

Solve the problem.

Question 66

Use the formula indicated to determine the prime number generated for the given value of n.

A)53
B)1847
C)3645
D)6847

Question 67

520 and 616 are amicable numbers.

Question 68

Determine whether the number is abundant or deficient.
8

A)Abundant
B)Deficient

Question 69

Determine whether the number is abundant or deficient.
18

A)Abundant
B)Deficient

Question 70

Twin primes are prime numbers whose difference is a multiple of 4.

Question 71

Determine whether the statement is true or false.

Question 72

Solve the problem.

Question 73

Determine whether the statement is true or false.

Question 74

A natural number which is not deficient must be abundant.

Question 75

Solve the problem.

Question 76

Not all perfect numbers end in 6 or 28.

Question 77

Solve the problem.

Question 78

There is no largest prime number.

Question 79

Determine whether the number is abundant or deficient.
30

A)Abundant
B)Deficient

Question 80

Determine whether the number is abundant or deficient.
95

A)Deficient
B)Abundant