**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.

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**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.

we can also check by 6n+1 divide by 6, if remainder 1 than its prime number.