Types of Number

Natural Number

Any number that matches the numbers those starts from \(1, 2, 3, 4, ….\) is called a Natural Number or Counting number.

Example

\(4, 9 , 11, 35, 99, 500\) or \(9876\) are natural numbers.

Whole Number

Any number that matches the numbers those starts from \(0, 1, 2, 3, 4, ….\) is called a Whole Number.

Example

\(0, 2, 14 , 23, 48, 172, 623\) or \(1245\) are whole numbers.

Integers

All natural numbers and negative of natural numbers including zero are called Integers.

Example

\(-65, -12, -5, 0, 56, 89\) or \(354\) are Integers.

Note

Zero is neither a negative number nor positive number. It is a neutral number.

Rational Numbers

The numbers each of which can be expressed in the form of \(\frac{p}{q}\), where p and q are integers and q is not equal to zero, are called Rational Numbers. Besides, the rational numbers are also non terminating and repeating numbers.

Example

\(\frac{2}{5}\), \(\frac{1}{3}\), \(\frac{8}{9}\), \(\frac{3}{10}\) etc.

Irrational Numbers

The numbers which are not rational are called irrational numbers. Besides, irrational numbers are also non terminating and non repeating numbers.

Example

\(\sqrt 2\), \(\sqrt 5\) etc.

Real Numbers

Set of rational numbers and irrational numbers is called Real Numbers.

Example

\(\sqrt 7\), \(\frac{1}{8}\), \(\frac{3}{10}\) etc.

Prime Number

Any Natural number greater than \(1\), which is divisible by \(1\) and only by itself is called Prime Number.

Example

\(2\), \(3\), \(5\), \(7\), \(11\) etc.

Note

\(2\) is the smallest Prime Number.

Composite Number

Any Natural number, which is greater than \(1\) and is not a Prime Number is called a Composite Number.

Example

\(4\), \(6\), \(8\), \(9\), \(10\) etc.

Note

\(1\) is neither a Prime Number nor Composite Number.

Coprimes

Two numbers are called to be coprime or co-prime if they have only \(1\) as common factor.

Example

\((2,3)\), \((14,15)\), \((8,13)\) etc.

Twin Primes

Two numbers are called Twin Primes if they differ by 2 only or we can say that there is only one composite number between them.

Example

\((3,5)\), \((29,31)\), \((71,73)\) etc.

Prime Triplets

A set of three consecutive Prime Numbers if they differ by 2, is called a Prime Triplet.

Example

\((3,5,7)\) etc.