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 maths negative numbers and integers odd and even numbers operations on integers different types of numbers

The numbers which are not multiples of $2$ are called _______.

  1. even

  2. odd

  3. prime

  4. composite
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The numbers $1,3,5,7,9$ etc are called odd number which is not divisible by $2$ and any number which ends which these numbers are also called odd number. 

So, the numbers which are not multiples of $2$ are called odd.
Hence, the answer is odd.

Multiple choice mathematical modelling proof by contradiction similar triangles

To prove "" All prime numbers are not odd."  we showed that "$2$ is even and prime"
This method is  

  1. The Direct method.

  2. The proof by contradiction.

  3. Induction method.

  4. The proof by giving counter example.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

counterexample is a special kind of example that disproves a statement or proposition.hence it disproves that all prime numbers are odd hence it is proof by counter example

$D$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

The numbers which are multiples of $2$ are called ____.

  1. odd

  2. even

  3. prime

  4. composite
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The numbers $2,4,6,8,10$ are known as even number. 

The numbers which are completely divisible by $2$ are known as even numbers.
So, the numbers which are multiples of $2$ are called even numbers.

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

L.C.M. of two co-prime numbers is their

  1. sum

  2. difference

  3. product

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

The two numbers which have only 1 as their common factor are called co-primes.

For example, Factors of $ 5 $  are $ 1, 5 $
Factors of $ 3 $ are $ 1, 3 $

Common factors is $ 1 $.
So they are co-prime numbers.

To find their LCM, we

then choose each prime number with the greatest power and multiply them to get the LCM.
$ => LCM = 3 \times 5 = 15 $

Hence, LCM of two co-prime numbers is their product.

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

Every number is a ...... and a ........ of itself.

  1. factor, multiple

  2. prime, composite

  3. even, odd

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Every number is a factor and a multiple of itself. 

For example, $ 10 $ has a factor $ 10 $ as well as a multiple $ 10. $

Multiple choice maths set concepts finite and infinite sets types of sets set language

Which one of the following sets is infinite?

  1. Set of all integers greater than $5$
  2. Set ofall integers between $-10^{10}$ and $+10^{10}$
  3. Set of all prime numbers between $0$ and $10^{100}$

  4. Set of all even prime numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(2), (3), and (4) are finite sets.

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

The sum of the powers of the prime factors in $108 \times 192$  is

  1. $5$
  2. $7$
  3. $8$
  4. $12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle 108=2\times 2\times  3\times 3\times 3=2^{2}\times 3^{3}$
$\displaystyle 192=2\times2\times2\times2\times2\times2\times3$
$\displaystyle =2^{6}\times 3^{1}$
$\displaystyle 108 \times 192=2^{2}\times 3^{3}\times 2^{6}\times 3^{1}$
$\displaystyle =2^{8}\times 3^{4}$
Sum of the powers = 8 + 4 = 12

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

Let A = { even number} B = {prime numbers} Then A $\displaystyle\cap $ B equals: 

  1. {odd number}

  2. {composite number}

  3. {2}

  4. {whole numbers}
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given: A = ${2, 4, 6, ...}$
     B = ${2, 3, 5, ...}$
$\displaystyle \therefore $ 2 is the only even prime number $\displaystyle A\cap B=\left { 2 \right }$

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

Let $P _1$ be the set of all prime numbers, i.e., $P _1=\left {2, 3, 5, 7, 11, ....\right }$, Let $Pn=\left {np|p\epsilon P _1|\right }$, i.e., the set of all prime multiples of n. Then which of the following sets is non empty?

  1. $P _1\cap P _{23}$
  2. $P _7\cap P _{21}$
  3. $P _{12}\cap P _{20}$
  4. $P _{20}\cap P _{24}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Check by option
$P _{12}=\left {24, 36, 60, 84, ....\right }$
$P _{20}=\left {40, 60, 100, .....\right }$
$P _{12}\cap P _{20}$ has common element.