When a number is divisible by only one and itself, then it is a prime number. The prime numbers cannot be factorised as they do not have factors other than 1 and the number itself. The numbers with more than two factors are called composite numbers. 1 is neither prime nor composite.

Method 1:

Every prime number can be written in the form of 6n + 1 or 6n – 1 (except the multiples of prime numbers, i.e. 2, 3, 5, 7, 11), where n is a natural number.

Method 2:

To know the prime numbers greater than 40, the below formula can be used.

n² + n + 41, where n = 0, 1, 2, ….., 39

How do we get to know if a number is prime or not?

To identify the prime number, we need to find the factors of the number. For example, take a number; 11, 11 is divisible only by 1 and itself. Since it has only two factors, it is a prime number.

Solved Examples

Question 1: Find if 53 is a prime number or not.

Solution:

The factors of 53 are 1 and 53.
So 53 is only divisible by 1 and 53.
Therefore, 53 is a prime number.

Question 2: Check if 64 is a prime number or not.

Solution:

The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

64 has more than 2 factors.
Hence, it is a composite number but not a prime number.