Is 1 a prime number

 As a teacher, usually we meet a heterogeneous group of students in our class. In result of this, we face a big pool of questions when we introduce a concept in the class we are teaching.

A student of mine recently surprised me by saying that he was not sure whether the number 1 was prime number or not.

So, Let us try to clear everyone’s confusion regarding the same topic. 

First of all we understand numbers.

{1,2,3,4,5,6—} are Natural numbers. It is denoted by N.

If we add zero to Natural numbers the result will be Whole numbers. {0,1,2,3,4,5,6,7—} are Whole numbers. It is denoted by W.

The collection of positive numbers and negative numbers with zero {— -5,-4,-3,-2,-1,0,1,2,3,4,5—} is called Integers. It is denoted by Z.

We also know about Even numbers and Odd numbers. Even numbers are {2,4,6,8—}. The numbers which are divisible by 2 are called Even numbers. Odd numbers are {1,3,5,7,9—}. The numbers which are not divisible by 2 are called Odd numbers.

The confusion begins with the definition of Prime numbers.

“A Prime number is a positive whole number that is only divisible by 1 and itself”

This definition has been published with proofs from scientists and is not random. Therefore, it is not our choice to understand the concept according to us.

Let’s see some numbers-

1=1*1

2=2*1

3=3*1

4=1*2*2,1*4 and 2*2

5=5*1

6=6*1,3*2 and 1*2*3

 In above examples, it can be seen that the number 4 and 6 have multiple ways of factorization.

We can see the factors of 2,3 and 5 they have single way of factorization (2=2*1,3=3*1).

But in case of 1-the number 1 is divisible by 1 and it is also divisible by itself, but, itself and 1 are not distinct factors (both are the same).The definition says that- Prime numbers must have exactly two distinct factors (different numbers) 1 and itself. But in case of ‘1’ both numbers are the same, therefore, there is no distinction in its factors.Therefore,1 is not a prime number.

2 is the smallest prime number that satisfies the definition of prime number,  that is, there are two distinct factors of the number ‘2’- which are 2 and 1 respectively. Similarly, .3,5,7,11—follow the suit.

Hopefully , the explanation is clear. Thanks to the  student for asking this question and helping everyone learn more about the confusing topic.

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