How is One a factor of every number?

Property

One is always a factor of every number.

Introduction

Let’s first know two important facts about the number $1$.

The number $1$ is a first natural number and it represents a whole quantity.
The number $1$ has a natural property and it allows the number $1$ to divide every whole number completely.

According to the mathematical definition of a factor, if a number divides another number completely, then the number is called a factor of that other number. In mathematics, the number $1$ divides every whole number completely. So, the number $1$ is called a factor of every number.

Proof

Let’s prove why the number $1$ is a factor of every number, with two simple arithmetic examples.

Example: 1

$6 \div 1$

Let’s divide the number $6$ by the number $1$

$=\,\,$ $\dfrac{6}{1}$

$=\,\,$ $6$

The natural number $1$ completely divides the number $6$. So, the number $1$ is a factor of number $6$.

Example: 2

$13 \div 1$

Let’s divide the number $13$ by the number $1$

$=\,\,$ $\dfrac{13}{1}$

$=\,\,$ $13$

The number $1$ completely divides the number $13$. So, the number $1$ is a factor of number $13$.

The above two examples proved that the number one can divide any number completely.

You can repeat same procedure to divide any number by $1$ and you will observe that the number $1$ divides that number completely.

Therefore, it is proved that the number $1$ is a factor of every number.

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