Number Theory Worksheet
(Answers at the end)
1. What is the smallest prime number?
A) 0
B) 1
C) 2
D) 3
2. What is the greatest common divisor (GCD) of 56 and 98?
A) 14
B) 7
C) 28
D) 49
3. The least common multiple (LCM) of 12 and 18 is:
A) 36
B) 72
C) 54
D) 108
4. If a number is divisible by 2, 3, and 5, it must be divisible by:
A) 10
B) 15
C) 30
D) 60
5. Which of the following numbers is a perfect square?
A) 36
B) 50
C) 72
D) 85
6. What is the sum of the first five prime numbers?
A) 18
B) 28
C) 26
D) 30
7. A number that is not divisible by any number other than 1 and itself is
called a:
A) Composite number
B) Even number
C) Odd number
D) Prime number
8. Which of the following is a factor of every even number?
A) 1
B) 2
C) 3
D) 5
9. The sum of two odd numbers is:
A) Odd
B) Even
C) Prime
D) Composite
10. What is the value of the Euler's totient function ϕ(9)?
A) 3
B) 6
C) 9
D) 4
11. The last digit of the number 31003^{100}3100 is:
A) 1
B) 3
C) 7
D) 9
12. What is the sum of the digits of 2^15?
A) 26
B) 27
C) 28
D) 29
13. Which number is neither prime nor composite?
A) 0
B) 1
C) 2
D) 3
14. The sum of two numbers is 24 and their GCD is 4. The numbers are:
A) 4, 20
B) 8, 16
C) 12, 12
D) 10, 14
15. How many positive divisors does the number 60 have?
A) 10
B) 12
C) 6
D) 8
16. If p is a prime number greater than 3, then p2−1p^2 - 1p2−1 is:
A) Divisible by 6
B) Divisible by 12
C) Divisible by 24
D) Divisible by 36
17. Which of the following is a prime number?
A) 39
B) 51
C) 53
D) 57
18. The product of the first four prime numbers is:
A) 30
B) 210
C) 2310
D) 969
19. The largest prime factor of 91 is:
A) 7
B) 13
C) 17
D) 19
20. If the sum of the digits of a number is divisible by 9, then the number
itself is:
A) Divisible by 9
B) Divisible by 3
C) Even
D) Prime
21. What is the number of positive integers less than 100 that are relatively
prime to 100?
A) 20
B) 40
C) 50
D) 60
22. The decimal representation of the fraction 17\frac{1}{7}71 is:
A) Terminating
B) Non-terminating, repeating
C) Non-terminating, non-repeating
D) None of the above
23. The remainder when 51005^{100}5100 is divided by 7 is:
A) 1
B) 2
C) 3
D) 4
24. What is the smallest positive integer n such that n2n^2n2 ends with the
digits 900?
A) 30
B) 50
C) 60
D) 90
25. The number of zeros at the end of 100! (100 factorial) is:
A) 24
B) 25
C) 22
D) 20
26. If a and b are two integers such that their sum and product are both odd,
which of the following is true?
A) Both a and b are even
B) Both a and b are odd
C) One is odd and one is even
D) a is even and b is odd
27. The sum of the first n odd natural numbers is:
A) n2n^2n2
B) n(n+1)n(n + 1)n(n+1)
C) 2n+12n + 12n+1
D) n(n−1)n(n - 1)n(n−1)
28. What is the 50th prime number?
A) 227
B) 229
C) 233
D) 239
29. The modular inverse of 5 modulo 7 is:
A) 1
B) 2
C) 3
D) 5
30. Which of the following numbers is a Carmichael number?
A) 341
B) 561
C) 1105
D) All of the above
Answers
1. C 11. A 21. B
2. A 12. B 22. B
3. A 13. B 23. C
4. C 14. B 24. C
5. A 15. B 25. B
6. D 16. B 26. B
7. D 17. C 27. A
8. B 18. B 28. C
9. B 19. B 29. D
10. B 20. A 30. D
