A prime number is an integer greater than one and can be divisible by only itself and one i.e it has only two factors. Zero, 1, and numbers less than 1 are not considered as prime numbers.

A number having more than two factors are referred to as composite numbers. The smallest prime number is 2 because it is divisible by itself and 1 only.

To check whether any number is a prime number or not first we have to take factors of that number. If it has only two factors that are the number itself and 1 then it is a prime number. The following are the steps to check whether the given number is prime or not.

To check whether the number is a prime number, first, divide the number by 2 if it is completely divisible by 2 it is not a prime number but if it is not divisible by 2, try with 3. Take the square root of a number and check the division test till the number less than the square root. If it is not divisible by any number then it is a not prime number or else it is a prime number. So let us check if 91 is a prime or composite number?

Now let us follow this step for 91 and see if 91 is a prime number or not.

To find whether 91 is prime or composite, first, check whether (9+1) is divisible by 2 if no check it by 3.

We have, 9+1 is 10 which is not divisible by 3, continue with the following steps.

Step 1: First take the square root of 91, \[\sqrt{91}\] = 9.53

Step 2: Choose prime numbers less than 9 and see if any of the numbers divide 91 completely.

Step 3: we get that the number 7 divides 91 perfectly. So, 91 is divisible by 7 we get more than two factors other than 1 and 91 itself. Hence, we can say that 91 is not a prime number.

So, why 91 is not a prime number is because it has more than two factors which contradict the definition of prime numbers.

As we can see why is 91 not a prime number it is because it has more than two factors other than 1 and the number itself. It contradicts the definition of prime numbers. So 91 is a composite number because composite numbers have factors more than 2.

When we factorize 91 we get

91 ÷ 1 = 91

91 ÷ 7 = 13

91 ÷ 13 = 7

91 ÷ 91 = 1

Here we get four factors for 91 and they are 1, 13, 7, 91. As the total number of factors are more than two it satisfies the condition of composite number. Hence 91 is a composite number.

Now it is clear that 91 does not satisfy the conditions of prime numbers. It satisfies the conditions for composite numbers so 91 is a composite number.

Some other kind of numbers in which 91 falls are as follows

A natural number

A positive integer

An odd number

A rational number

A composite number

A whole number

Example 1: Is 19 a Prime Number or not?

Solution:

We can check the number is prime or not in two ways.

Method 1:

The formula for the prime number is 6n + 1

Let us write the given number in the form of 6n + 1.

6(3) + 1 = 18 + 1 = 19

Method 2:

Check for the factors of 19

19 has only two factors 1 and 19.

Therefore, by both the method we get 19 is a prime number.

Example 2: Is 53 is a prime number or not?

Solution:

Method 1:

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

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

Put n= 3

32 + 3 + 41 = 9 + 3 + 41 = 53

Method 2:

53 has only factors 1 and 53.

So, 53 is a prime number by both the methods.

FAQ (Frequently Asked Questions)

1. Is 1 a Prime Number or Composite Number?

Answer : 1 is neither a prime number or a composite number because 1 is divisible by only itself, thus it has only 1 factor. Hence it contradicts both the definition of a prime number and composite number. They both have more than two factors.

2. What is the Difference Between Prime Numbers and Composite Numbers?

Answer: A prime number has only two factors that is the number itself and one, while a composite number has more than two factors.

A prime number is divisible by only 1 and by itself, while the composite number is divisible by all its factors.

For example, 2 is a prime number it is divisible by 1 and 2 itself 9 is a composite number, it has three factors 1, 3, and 9 and it is divisible by all its factors.

3. What is the Formula to Find the Prime Numbers?

Answer: There are two methods to find whether the given number is prime or not

Method 1:

Two consecutive natural numbers which are prime are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.

For example:

6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13…so on

Method 2:

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

n2+ n + 41, where n are natural numbers 0, 1, 2, ….., 39

For example:

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47…..so on