We know that an integer n>1 is said to
be a prime if it has no divisor other than ±1 and ±n itself.
That is if b|n and b>1, then b is =n ----------{ here
b|n means b divides n.}
Example:- 2,3,5,7,11,,,,,,,,,,,,etc.
There is only one even prime number namely 2.
In other hand,
An
integer n>1 is said to be composite if it is not a prime.
Note
that 1 is
neither a prime nor a composite; the natural numbers greater than 1 are divided
into two groups, namely primes and composites.
Now, if n is composite or not prime, then n has a divisor greater
than 1. If p is the least divisor of n and p>1, then p is necessarily a
prime. It follows that every integer greater than 1 is either a prime or has a
prime divisor.
If p is a prime dividing n.
That is;
If p|n, then n = px, where ……………….. 1 ≤ x ≤n.
Here if x = 1 then n is a prime, and if x>1 then we can write x as
a product of prime p and x’ Like x = px’.
Thus, we see that every integer greater than 1 is either a prime or a product of primes.
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