Prime Numbers and Composite Numbers

How to check whether a number is prime or not?

To check whether a given number N is prime or not, first find the square root of that number N and then approximate that to immediately lower integer (say n) and write down all the prime numbers less than that integer (n). Then check the divisibility of the given number N by all the prime numbers we have written in previous step, if it is not divisible by any of the prime numbers then given number N is prime.

Let us write algorithm for the same
Step 1: Find square root of N, call it as K (Just find approximate values)
Step 2: Write down all the prime numbers less than K.
Step 3: Check divisibility of N with these prime numbers, which we have got in Step 2.
Step 4: If N is not divisible by any of the prime numbers then N is prime.

Example:
Let us check whether 211 is prime or not?
Solution:
Step 1: We find square root of 211 i.e. K=√211  = 14.52
Step 2: We write all primes less than 14.52 i.e. 2, 3, 5, 7, 11 and 13.
Step 3:Since 211 is not divisible by any of these prime numbers, hence 211 is a prime number.
 

Example:
Let us check whether 313 is prime or not?
Solution:
Step 1: We find square root of 313 i.e. K=√311  = 17.69
Step 2: We write all primes less than 17.69 i.e. 2, 3, 5, 7, 11, 13 and 17
Step 3:Since 313 is not divisible by any of these prime numbers, hence 313 is a prime number.

Composite numbers
Number which is the product of two or more than two distinct or same prime numbers is said to be composite number Or we say that if a number has more than two factors then it is said to be a composite number.
For example 4, 6, 8, 15………..are all composite numbers
We can write 4 = 2 × 2,
6 = 2 × 3.
Some points to remember

• 1 is neither prime nor composite.
• 2 is the only prime number which is even. Rest all prime numbers are odd.