PRIME AND COMPOSITE NUMBERS

PRIME AND COMPOSITE NUMBERS
1.    Observe the number of factors of some numbers arranged in the following table

We can see that
i)    The number ‘1’ has one and only one factor  (i.e., itself)
ii)    There are numbers having exactly two factors 1 and the number itself. we can see that such numbers are 2, 3, 5, 7, 11 etc.
    These numbers are said to be prime numbers
Definition:- 
    The number which has only factors 1 and itself is called prime number.
Note :- 
    ‘2’ is only even prime number
iii)     There are numbers which have more than two factors like 4, 6, 8, 9, 10 etc and so on are called composite numbers.
iv)    A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Definition:- 
     Numbers having more than two factors are called composite numbers.
Note :- 
    ‘1’ is neither prime nor composite number.
Note :- 
    A composite number is a natural number greater than 1 that is not a prime number.
By using the method of sieve of eratosthenese easily we can verify the whether the given number is prime or not