250+ TOP MCQs on Number Theory and Answers

Cryptography Multiple Choice Questions on “Number Theory”.

1. If a|b and b|c, then a|c.
a) True
b) False

Answer: a
Clarification: The statement is true. For ex, 11|66 and 66|198 = 11|198.

2. GCD(a,b) is the same as GCD(|a|,|b|).
a) True
b) False

Answer: a
Clarification:This is true. gcd(60,24) = gcd(60,-24) = 12.

3. Calculate the GCD of 1160718174 and 316258250 using Euclidean algorithm.
a) 882
b) 770
c) 1078
d) 1225

Answer: c
Clarification: GCD(1160718174, 316258250) = 1078.

4. Calculate the GCD of 102947526 and 239821932 using Euclidean algorithm.
a) 11
b) 12
c) 8
d) 6

Answer: d
Clarification: GCD(102947526, 239821932) = 6.

5. Calculate the GCD of 8376238 and 1921023 using Euclidean algorithm.
a) 13
b) 12
c) 17
d) 7

Answer: a
Clarification: GCD(8376238, 1921023) = 13.

6. What is 11 mod 7 and -11 mod 7?
a) 4 and 5
b) 4 and 4
c) 5 and 3
d) 4 and -4

Answer: d
Clarification:11 mod 7 = 4 ; -11 mod 7 = -4 mod 7 = 3 mod 7.

7. Which of the following is a valid property for concurrency?
a) a = b (mod n) if n|(a-b)
b) a = b (mod n) implies b = a (mod n)
c) a = b (mod n) and b = c (mod n) implies a = c (mod n)
d) All of the mentioned

Answer: d
Clarification: All are valid properties of congruences and can be checked by using substituting values.

8. [(a mod n) + (b mod n)] mod n = (a+b) mod n
a) True
b) False

Answer: a
Clarification: The equivalence is true and can be checked by substituting values.

9. [(a mod n) – (b mod n)] mod n = (b – a) mod n
a) True
b) False

Answer:b
Clarification:The equivalence is false and can be checked by substituting values. The correct equivalence would be [(a mod n) – (b mod n)] mod n = (a – b) mod n.

10. 11⁷ mod 13 =
a) 3
b) 7
c) 5
d) 15

Answer: d
Clarification: The correct answer is 2. Or in this case 15 mod 13 = 2.

11. The multiplicative Inverse of 1234 mod 4321 is
a) 3239
b) 3213
c) 3242
d) Does not exist

Answer: a
Clarification: The multiplicative Inverse of 1234 mod 4321 is 3239.

12. The multiplicative Inverse of 550 mod 1769 is
a) 434
b) 224
c) 550
d) Does not exist

Answer: a
Clarification: The multiplicative Inverse of 550 mod 1769 is 550.

13. The multiplicative Inverse of 24140 mod 40902 is
a) 2355
b) 5343
c) 3534
d) Does not exist

Answer: d
Clarification: The multiplicative Inverse does not exist as GCD (24140, 40902) = 34.