## Types of Numbers( Real numbers,Natural numbers,Whole numbers etc)

### Types of Numbers

**Real numbers:**Real numbers comprise the full spectrum of numbers.

They can take on any form – fractions or whole numbers, decimal points

or no decimal points. The full range of real numbers includes decimals

that can go on forever and ever without end.

For Example: 8, 6, 2 + , 3/5 etc.

**Natural numbers:**A natural number is a number that comes naturally.

Natural Numbers are counting numbers from 1, 2, 3, 4, 5, ……..

**Whole numbers:**whole numbers are just all the natural numbers plus zero.

For Example: 0, 1, 2, 3, 4, 5, and so on up to infinity.

**Integers:**Integers incorporate all the qualities of whole numbers and their opposites

(or additive inverses of the whole numbers) .

Integers can be described as being positive and negative whole numbers.

For Example: … –3, –2, –1, 0, 1, 2, 3, . . .

**Rational Numbers:**All numbers of the form p/q where p and q are integers

(q ≠ 0) called Rational numbers.

For Example: 4, 3/4, 0, ….

**Irrational Numbers:**Irrational numbers are the opposite of rational numbers.

An irrational number cannot be written as a fraction,

and decimal values for irrational numbers never end and do not have a repeating

pattern in them. ‘pi’ with its never-ending decimal places, is irrational.

For Example:

**Even Numbers:**An even number is

one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.

**Odd Numbers:**An odd number is one that does not divide evenly by two,

such as 1, 3, 5, and 7.

**Prime Number:**A prime number is a number which can be divided only by 1 and itself.

The prime number has only two factors, 1 and itself.

For example: 2, 3, 7, 11, 13, 17, …. are prime numbers.

**Composite Number:**A Composite Number is a number which can be divided evenly.

Any composite number has additional factors than 1 and itself.

For example: 4, 6, 8, 9, 10 …..

**Co-primes or Relatively prime numbers:**A pair of numbers not having any common

factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)

For Example: 15 and 28 are co-prime, because the factors of 15 (1,3,5,15) , and the factors

of 28 (1,2,4,7,14,28) are not in common (except for 1) .

of 28 (1,2,4,7,14,28) are not in common (except for 1) .

**Twin Primes:**A pair of prime numbers that differ by 2 (successive odd numbers that are

both Prime numbers) .

For Example: (3,5) , (5,7) , (11,13) , …

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