Discrete Mathematics Multiple Choice Questions on “Number Theory – Primes and Greatest Common Divisors”.
1. The prime factorization of 7007 is __________
a) 73.11.13
b) 72.11.13
c) 7.11.13
d) 7.113.13
Answer: b
Clarification: Perform successive division beginning with 2.
2. Out of following which one is Mersenne Primes?
a) 3
b) 7
c) 2047
d) 31
Answer: c
Clarification: 2047 = 23.89 also not in form of 2b-1 form.
3. Out of the following which of these integers is not prime?
a) 21
b) 35
c) 71
d) 101
Answer: b
Clarification: 35 = 5.7 which is the product of two prime numbers.
4. The prime factorization of 1001 is __________
a) 73.11.13
b) 72.11.13
c) 7.11.13
d) 7.113.13
Answer: c
Clarification: Perform successive division beginning with 2.
5. Which positive integer less than 21 are relatively prime to 21?
a) 18
b) 19
c) 21
d) 24
Answer: b
Clarification: gcd(19,21) = 1. According to the definition of relatively prime gcd of two numbers is 1.
6. Is 7, 8, 9, 11 are pairwise relatively prime.
a) True
b) False
Answer: a
Clarification: gcd(7, 9) = gcd(8, 9) = gcd(9, 11) = gcd(11, 7) = 1. The numbers 7 and 11 are prime and numbers 8 and 9 are relatively prime.
7. The greatest common divisor of 313.517 and 212.35 is __________
a) 30
b) 31
c) 33
d) 35
Answer: d
Clarification: gcd(a, b) = 3min(13, 5).5min(17, 0).2min(12, 0).
8. The greatest common divisor of 0 and 5 is ___________
a) 0
b) 1
c) 2
d) 5
Answer: b
Clarification: gcd(0, 5) = 0min(1, 0).5min(0, 1).
9. The lcm of 3 and 21 is ________ if gcd(3,21)=3.
a) 3
b) 12
c) 21
d) 42
Answer: c
Clarification: 3 * lcm(3, 21) = 63 hence, lcm(3, 21) = 63 / 3 = 21.
10. The least common multiple of 41.42 and 42.41 is ____________
a) 42
b) 41
c) 84
d) 41.42
Answer: d
Clarification: lcm(41 * 42, 42 * 42) = 41.42.42.41 / 41.42 = 41.42.