# What is a Prime number?

## Definition

A natural number that is divisible only by both one and itself is called a prime number.

### Introduction

There are infinite natural numbers and every natural number is divisible by either one or more natural numbers but some natural numbers, which are primarily divisible only by one and itself. So, those natural numbers are called the prime numbers.

Now, let’s learn clearly from some examples that what a prime number is.

$(1).\,\,$ The natural number $1$ is not a prime number.

$\implies$ $1 \div 1$ $\,=\,$ $1$

$(2).\,\,$ The natural number $2$ is a prime number because it is completely divisible only by $1$ and $2$.

$\implies$ $2 \div 1$ $\,=\,$ $2$ and $2 \div 2$ $\,=\,$ $1$

$(3).\,\,$ The natural number $3$ is a prime number because it is completely divisible only by $1$ and $3$.

$\implies$ $3 \div 1$ $\,=\,$ $3$ and $3 \div 3$ $\,=\,$ $1$

$(4).\,\,$ The natural number $4$ is not a prime number because it is completely divisible only by $1$ and $4$ but it is also divisible by $2$.

$\implies$ $4 \div 1$ $\,=\,$ $4,$ $4 \div 2$ $\,=\,$ $2$ and $4 \div 4$ $\,=\,$ $1$

$(5).\,\,$ The natural number $5$ is a prime number because it is completely divisible only by $1$ and $5$.

$\implies$ $5 \div 1$ $\,=\,$ $5$ and $5 \div 5$ $\,=\,$ $1$

The above examples help you to understand the fundamental definition of a prime number. In this way, the prime numbers can be identified from the infinite natural numbers in mathematics.

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