Is 1 A Prime Number?

There are 2 types of numbers - 

• Prime numbers

• Composite Numbers

Here, the number itself is the factor of 1, we can see that from the prime factorization method. A number needs to have at least two factors for it to be regarded as prime; this one only has one factor. So it can't be prime.

A number needs to satisfy 2 requirements to be prime.

The number should have only 2 divisors: 1 and the number itself .

• A number is a factor of only 2 numbers.

•    If all these above conditions are satisfied then only the numbers are taken as prime

To check for prime numbers, different methods are adopted -

• Divisor Counting Method

• Test for Divisibility

• Table for Prime Numbers

• Prime Factorization
   

Here, we will count the number of divisors a number has to check if it is a prime number. Now, let's look whether number 1 satisfies all conditions when we apply this.

Divisor of 1=1 

Number of divisors=1 

Hence, we can say 1 is not a prime number.
 

In this method, we will check whether the number is divisible by other numbers except 1 and the number itself. Let us check if the number 1 is divisible by 2,3,4,5 and 7. 

• To check whether a number is divisible by 2, the number should end with an even number. Here 1 is an odd number. So it is not divisible by 2.

• We say a number is divisible by 3, if the sum of the digits for that number is a multiple of that number. Here, 1 is not a multiple of 3. We can say 1 is not divisible by 3.

• If the last two digits form a multiple of 4, the number is divisible by 4. Here, 1 ends with 1, which is not a multiple of 4. So, it is impossible to be divisible by 4.

• The number should end up with either 5 or 0 to divide by 5, and 1 does not end up with 5 or 0. Thus, it is inadmissible.

• Since 1 is less than 7, we can say that 1 cannot be divided by 7. The numbers in the above cannot be divided into 1. Only 1 can be divided into only 1. So, the number cannot be counted as prime number.
   

In this method we have to write down all the prime numbers that arise between 1 and 100. If any number arises in this list, then it is a prime number. The prime numbers between 1 and 100. 
 

Applying this method, we break the large numbers into small numbers to check the factors. This method is applicable only for composite numbers.

If we apply the above procedure we note for the number 1, only one factor is 1. So number 1 cannot be a prime number.
 

• Factor: A number that divides another number exactly and leaves no remainder.

• Divisor: A number by which another number is divided is called divisor.

• Composite number: If the number of factors for the given number is above 2, then that number is a composite number.

• Natural Number: All the positive numbers from 1 towards infinity are natural numbers.