Is 91 a Prime Number?

Prime numbers are the numbers that have only two factors, the number itself and 1. 

To check if a number is prime or not we have to factorize it. So let us study whether 91 is a prime or composite number or why is 91, not a prime number? After factorizing 91, we get 4 factors. 91 has more than 2 factors i.e 1, 7,13, and 91 so 91 is not a prime number. In this article we will be studying what are prime numbers, how to determine a number, is prime or not, and is 91 a prime number?

What is a Composite Number?

Numbers containing more than two elements are called composite numbers. The number of components that a number has can be used to classify it. A prime number is one that contains just two factors: one and the number itself. Most numbers, however, include more than two elements and are referred to as composite numbers. We'll look at the distinction between prime and composite numbers, as well as the lowest composite number and odd composite numbers, on this page. The last one is intriguing because, unlike 2, which is the only even prime number, there exist multiple odd composite numbers.

What is the Prime Number?

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 prime numbers.

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

Steps to Check Prime Number

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 is 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. 

Properties of a Prime Number

A prime number is a positive integer with two components that are precisely the same. If p is a prime, then the only factors it can have are 1 and p. A composite number is one that does not follow this pattern and maybe factored into other positive integers. A positive number or integer that is not a product of any other two positive integers other than 1 and the number itself is another method of describing it.

It's worth noting that 1 is a non-prime number. It's a one-of-a-kind number.

List of prime numbers to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

91 a Prime Number or Not

To find whether 91 is prime or composite, first, check whether (9+1) is divisible by 2 if not 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, 91−−\[\sqrt{}\] = 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 that contradict the definition of prime numbers.

91 is a Prime or Composite Number

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 is more than two it satisfies the condition of a composite number. Hence 91 is a composite number.

What Kind of Number is 91 Then?

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 kinds 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

Solved Examples

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 methods, we get 19 as 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.