Mathematics · Quantitative Aptitude

Number Theory

438 Questions

Number theory explores the properties and relationships of integers, focusing heavily on prime and composite numbers. Key areas include identifying prime numbers, understanding co primes, and exploring mathematical conjectures like Goldbach's. These questions are a core component of quantitative aptitude sections in banking and government exams.

Prime number identificationCo prime propertiesGoldbach conjectureOdd and even numbersDivisibility rules

Number Theory Questions

Multiple choice general knowledge

What is the lowest prime number?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A prime number must have exactly two distinct factors: 1 and itself. 2 is the lowest prime number (factors: 1, 2). 0 has infinite factors, 1 has only one factor, and while 3 and 5 are prime, they are not the lowest.

Multiple choice general knowledge

Once RAJINI, while sleeping, murmured some numbers..what do we call those numbers?

  1. series of prime numbers

  2. fibonassi series

  3. log table

  4. series of number divisible by 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a 'Rajinikanth joke' - a genre of internet humor in Indian culture that exaggerates the actor's abilities in absurd ways. The answer 'log table' is part of the joke claiming that even Rajinikanth's sleep murmuring produces something mathematically complex. These jokes are meant to be humorous and not factual.

Multiple choice general knowledge math & puzzles

least prime number

  1. 1

  2. 2

  3. 3

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

2 is the least prime number because it is the smallest positive integer with exactly two distinct divisors (1 and itself). 1 is not prime by definition as it has only one divisor.

Multiple choice general knowledge

What is the next prime number after 7?

  1. 13

  2. 9

  3. 11

  4. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After 7, we check 8 (not prime, divisible by 2), 9 (not prime, divisible by 3), 10 (not prime, divisible by 2 and 5), and 11. 11 is prime because its only divisors are 1 and 11. Prime numbers are greater than 1 and only divisible by 1 and themselves.

Multiple choice general knowledge math & puzzles

What is the probability of choosing a prime number from the numbers 90 to 100 inclusive?

  1. 1 by 5

  2. 1 by 10

  3. 2 by 10

  4. 1 by 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The numbers from 90 to 100 inclusive are 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 (total 11 numbers). Among these, only 97 is a prime number. Therefore, the probability is 1 out of 11. Other options assume a total of 10 numbers, which is incorrect for an inclusive range.

Multiple choice general knowledge science & technology

What is the next prime no. after 7?

  1. 8

  2. 9

  3. 11

  4. 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Prime numbers are integers greater than 1 that have exactly two factors: 1 and themselves. After 7, the next integer is 8 (not prime, divisible by 2), then 9 (not prime, divisible by 3), then 10 (not prime, divisible by 2 and 5). The number 11 is prime because its only factors are 1 and 11. While 13 is also prime, it is not the next prime after 7.

Multiple choice softskills creativity

how will u find Prime No below N<=10^6 within 2 sec whereas the Processor speed is low , Ram capacity is also limited..

  1. sieve of Atkin

  2. Cheacking each number wherther it is prime or not

  3. Eratosthenes Sieve

  4. none of the above
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Both Sieve of Atkin and Eratosthenes Sieve efficiently generate all primes up to N using O(N log log N) time complexity. Eratosthenes works by iteratively marking multiples of each prime starting from 2, while Atkin uses quadratic forms to sieve composites. Both algorithms easily handle N=10^6 within 2 seconds even on modest hardware. Option B is inefficient (O(N*sqrt(N))) and would exceed the time limit.

Multiple choice

Consider the following formula and its two interpretations $I_1$ and $I_2$.

$\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]$

$I_1$ : Domain: the set of natural numbers

$P_x$ = 'x is a prime number' $Q_{xy}$ = 'y divides x' $I_2$ : same as $I_1$ except that $P_x$ = 'x is a composite number'.

Which of the following statements is true?
  1. I1 satisfies$\alpha$, I2 does not
  2. I2 satisfies $\alpha$, I1 does not
  3. Neither I2 nor I1 satisfies $\alpha$
  4. Both I1 and 12 satisfy $\alpha$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]$ I1: domain the set of natural numbers Px = x is a prime number = 2, 3, 5, 7, 11, 13… Qxy = y divides x = means y is also prime number = 2,3,5,7,11,13, I2: px = x is composite number (i.e not prime number) = 4,6,8,9,10,12,14,….. Qxy = 2,3,4,5,7,……. = mean all the numbers from expression, we know I1 satisfies $\alpha$,I2 does not

Multiple choice

In the RSA public key cryptosystem, the private and public keys are (e,n) and (d,n) respectively, where n=p*q and p and q are large primes. Besides, n is public and p and q are private. Let M be an integer such that 0<M<n and $\phi$ (n) = (p − 1) (q − 1). Now consider the following equations. I. M' = Me mod n
M = (M')d mod n II. Ed = 1 mod n III. ed = 1 mod $\phi$(n) IV. M' = Me mod $\phi$(n) M = (M')d mod $\phi$(n) Which of the above equations correctly represent RSA cryptosystem?

  1. I and II

  2. I and III

  3. II and IV

  4. III and IV
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation