# Types of Numbers

**Even Numbers****Odd Numbers****Prime Numbers****Composite Numbers****Twin Primes****Co Primes****Perfect Numbers****Square Numbers**

**Factor (Divisor):-**

**A factor of a number is the number that when divides the given numbers leaves no remainder.**

**If a number ‘a’ divides ‘b’ exactly we say that a is a factor of b and also we say that b is a multiple of a**

**Factors of 2 = 1, 2****Factors of 4 = 1, 2, 4****Factors of 5= 1, 5****Factors of 15= 1, 3, 5, 15****Factors of 50= 1,2,5,10,25,50**-
**1 is a factor of every number and is the smallest factor.** **Every number is a factor of itself and is the largest factor****The factor of a number is less than or equal to that number.**

# Multiples :-

### If a number is multiplied the natural numbers 1,2,3,.. then the products are called multiples of a given number.

- Multiples of 2 = 2, 4, 6, 8, 10, 12,14, ………
- Multiples of 5= 5, 10, 15, 20,25,……
- Multiples of 10= 10, 20, 30, 40, 50, 60, 70, ……

**Every number is a multiple of itself.****Every number is a multiple of one.****There are infinite number of multiples for a natural number**

**Even Numbers :- ****Which numbers are exactly divisible by 2 are called Even Numbers.**

**vAll multiples of 2 are called Even Numbers**

**vIf the Unit’s place digit (or Ones digit) is 2 or 4 or 6 or 8 or 0 then the number is called an even number .**

**vEx:- 48; 125; 60858**

**Odd Numbers :- A number is divided by 2 leaves the remainder is 1 are called odd numbers .**

**vWhich numbers are not Multiples of 2 is called odd numbers.**

**vIf the Unit’s place digit (or Ones digit)is 1 or 3 or 5 or ****7 or 9 then the number is called an odd number.**

**Prime numbers :** **the natural numbers which have only one and themselves as factors are ****called prime numbers ( or simply primes )**

## · Numbers which can not be divided by any number other than 1 and number itself are known as prime numbers

## · Which number has exactly two factors, namely 1 and itself, is called a prime number.

### Prime numbers below 100

### 2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37, 41,43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 etc. are all prime numbers.

**Composite Numbers :**

Numbers having more than two factors are known as composite numbers.

Numbers which can be divided by at least one of the number other than 1 and itself are known as composite numbers

A number which has at least one more factor other than 1 and itself is called composite number.

**1 is neither prime nor composite****2 is the lowest prime number****2 is the only even prime number, all other even number are composite numbers.****Any prime number greater than 2 is an odd number.****4 is the smallest composite number.****9 is the smallest odd composite number**

## ** v If the difference between a pair of prime numbers is 2 they are called Twin primes.**

**v Pair of twin primes between 1 and 100 are**

**(3,5 ), (5,7 ), (11, 13 ), ( 17, 19), **

**( 29, 31) ****(41, 43 ), (59, 61 ), **

**(71, 73 )**

# ** P****rime Triplet :- ****A set of three consecutive prime numbers, differing by 2 is called a prime triplet.**

**The only prime triplet is { 3, 5, 7}**

**Perfect Number:-**

**If the sum of all the factors of a number is two times the number then the number is called a perfect number.**

**6 is a perfect number, since the factor of 6 are 1, 2, 3, 6 and (1+2+3+6)= (2 ×6)**

**28 is a perfect number, since the factor of 28 are 1, 2, 4, 7, 14, 28 and****(1+2+4+7 +14+28)=(2 ×28)**