Is 2 a prime number?

The number two is a second natural number and let’s find whether the natural number $2$ is a prime number or not by the fundamental definition of a prime number.

According to the definition of a prime number, let’s observe what happens when the natural number $2$ is divided by both one and itself.

Divide the number 2 by 1

Firstly, let’s divide the natural number $2$ by the natural number $1$.

$2 \div 1$

$\implies$ $\dfrac{2}{1} \,=\, 2$

The natural number $2$ is completely divided by the $1$. So, the quotient of $2$ divided by $1$ is $2$. It clears that there is a chance for the natural number $2$ to become a prime number.

Divide the number 2 by itself

Now, let’s divide the natural number $2$ by the same natural number.

$2 \div 2$

$\implies$ $\dfrac{2}{2} \,=\, 1$

The natural number $2$ is completely divided by itself and the quotient of $2$ divided by $2$ is equal to $1$.

Conclusion

1. The number $2$ is completely divided by the number $1$.
2. The number $2$ is also completely divided by the same number.

It clears that the number $2$ is divisible only by one and itself. Therefore, the number $2$ can only be expressed as a product of one and itself.

$\implies$ $2$ $\,=\,$ $1 \times 2$

The number $2$ has only two factors and they are $1$ and $2$. It proves that the number $2$ is a prime number and it is a first prime number in the natural numbers.