Discrete Mathematics

Number Theory

Question 1
Marks : +2 | -2
Pass Ratio : 14%
Is 7, 8, 9, 11 are pairwise relatively prime.
True
False
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.
Question 2
Marks : +2 | -2
Pass Ratio : 14%
The lcm of 3 and 21 is ________ if gcd(3,21)=3.
3
12
21
42
Explanation:
3 * lcm(3, 21) = 63 hence, lcm(3, 21) = 63 / 3 = 21.
Question 3
Marks : +2 | -2
Pass Ratio : 14%
Out of following which one is Mersenne Primes?
3
7
2047
31
Explanation:
2047 = 23.89 also not in form of 2b-1 form.
Question 4
Marks : +2 | -2
Pass Ratio : 14%
The greatest common divisor of 0 and 5 is ___________
0
1
2
5
Explanation:
gcd(0, 5) = 0min(1, 0).5min(0, 1).
Question 5
Marks : +2 | -2
Pass Ratio : 14%
The prime factorization of 7007 is __________
73.11.13
72.11.13
7.11.13
7.113.13
Explanation:
Perform successive division beginning with 2.
Question 6
Marks : +2 | -2
Pass Ratio : 14%
Which positive integer less than 21 are relatively prime to 21?
18
19
21
24
Explanation:
gcd(19,21) = 1. According to the definition of relatively prime gcd of two numbers is 1.
Question 7
Marks : +2 | -2
Pass Ratio : 14%
The least common multiple of 41.42 and 42.41 is ____________
42
41
84
41.42
Explanation:
lcm(41 * 42, 42 * 42) = 41.42.42.41 / 41.42 = 41.42.
Question 8
Marks : +2 | -2
Pass Ratio : 14%
The prime factorization of 1001 is __________
73.11.13
72.11.13
7.11.13
7.113.13
Explanation:
Perform successive division beginning with 2.
Question 9
Marks : +2 | -2
Pass Ratio : 14%
Out of the following which of these integers is not prime?
21
35
71
101
Explanation:
35 = 5.7 which is the product of two prime numbers.
Question 10
Marks : +2 | -2
Pass Ratio : 14%
The greatest common divisor of 313.517 and 212.35 is __________
30
31
33
35
Explanation:
gcd(a, b) = 3min(13, 5).5min(17, 0).2min(12, 0).