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)