This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Primes and Greatest Common Divisors”.

1. The prime factorization of 7007 is ________.

a) 7^{3}.11.13

b) 7^{2}.11.13

c) 7.11.13

d) 7.11^{3}.13

View Answer

Explanation: Perform successive division beginning with 2.

2. Out of following which one is Mersenne Primes?

1) 3

b) 7

c) 2047

d) 31

View Answer

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

Explanation: 35 = 5.7 which is the product of two prime numbers.

a) 7

^{3}.11.13

b) 7

^{2}.11.13

c) 7.11.13

d) 7.11

^{3}.13

View Answer

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

Explanation: 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. Is it True or False?

a) True

b) False

View Answer

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 3^{13}.5^{17} and 2^{12}.3^{5} is _______.

a) 3^{0}

b) 3^{1/sup>
c) 33
d) 35
View Answer}

Explanation: gcd(a, b) = 3

^{min(13, 5)}.5

^{min(17, 0)}.2

^{min(12, 0)}.

a) 0

b) 1

c) 2

d) 5

View Answer

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

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

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

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