How to Find the Factors of a Number

Once you know what a factor is, you are ready to learn how to find the factors of a number mathematically. So, let’s learn how to find the factors of any number by a simple and understandable example.

Introduction

A number can be divided by any real number as per the division method in mathematics. The same division method can also be used to find the factors of any number. There are three simple steps to find the factors of a number.

1. Write the natural numbers in a row from one to that number.
2. Divide the number by the numbers range from $1$ to that number and find their corresponding quotients.
3. If the quotient is a natural number or an integer, then the number that divides a number is called a factor of that number. Otherwise, it is not a factor of that number.

The above three steps may confuse you theoretically, but you can easily understand here by a simple and understandable example.

Example

Let’s find the factors of a number $6$ to know how to find the factors of every number.

The first number in natural numbers is one. So, let’s write the numbers firstly from one to six in a row.

$1,$ $2,$ $3,$ $4,$ $5$ and $6$

Now, divide the number six by each of above numbers to find their corresponding quotient. The first number in natural numbers is one. So, let’s divide the six by one firstly.

$6 \div 1$

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

The quotient of $6$ divided by $1$ is equal to $6$, which is a natural number, and it is not a fraction or a decimal number. So, we say that the number $1$ divides $6$ completely. Due to this reason, the number $1$ is called a factor of $6$.

$6 \div 2$

$\implies$ $\dfrac{6}{2} \,=\, 3$

The number $2$ divides $6$ completely. So, the number $2$ is called a factor of $6$.

$6 \div 3$

$\implies$ $\dfrac{6}{3} \,=\, 2$

The number $3$ divides $6$ completely. So, the number $3$ is called a factor of $6$.

$6 \div 4$

$\implies$ $\dfrac{6}{4} \,=\, 1.5$

The number $4$ does not divide $6$ completely. So, the number $4$ is not a factor of $6$.

$6 \div 5$

$\implies$ $\dfrac{6}{5} \,=\, 1.2$

The number $5$ does not divide $6$ completely. So, the number $5$ is not a factor of $6$.

$6 \div 6$

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

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

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