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Types of Numbers |Different Types of Numbers

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 )

 Prime 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)
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