Primes & Greatest Common Divisors - Discrete Mathematics Questions and Answers

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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
View Answer

Answer: b
Explanation: Perform successive division beginning with 2.

2. Out of following which one is Mersenne Primes?
a) 3
b) 7
c) 2047
d) 31
View Answer

Answer: c
Explanation: 2047 = 23.89 also not in form of 2^b-1 form.

3. Out of the following which of these integers is not prime?
a) 21
b) 35
c) 71
d) 101
View Answer

Answer: b
Explanation: 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
View Answer

Answer: c
Explanation: 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
View Answer

Answer: b
Explanation: gcd(19,21) = 1. According to the definition of relatively prime gcd of two numbers is 1.

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6. Is 7, 8, 9, 11 are pairwise relatively prime.
a) True
b) False
View Answer

Answer: a
Explanation: 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
View Answer

Answer: d
Explanation: gcd(a, b) = 3^{min(13, 5)}.5^{min(17, 0)}.2^{min(12, 0)}.

8. The greatest common divisor of 0 and 5 is ___________
a) 0
b) 1
c) 2
d) 5
View Answer

Answer: b
Explanation: gcd(0, 5) = 0^{min(1, 0)}.5^{min(0, 1)}.

9. The lcm of 3 and 21 is ________ if gcd(3,21)=3.
a) 3
b) 12
c) 21
d) 42
View Answer

Answer: c
Explanation: 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
View Answer

Answer: d
Explanation: lcm(41 * 42, 42 * 42) = 41.42.42.41 / 41.42 = 41.42.

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