The process of finding the factors of a number is called the factorization of a number.

Firstly, you should know what a factor really is. Once you understand the concept of a factor then you are ready to learn how to find the factors of a number and the process of finding the factors of a number is called the factorization of a number (U.S English) or factorisation of a number (U.K English).

There is a simple procedure to find the factors of any number in mathematics and let’s know the steps of finding the factors of a number.

- Use the long division method to divide a number by each natural number (starts from $1$).
- Continue the process of division until we see a reminder.
- If there is a remainder, then the divisor number cannot be a factor of dividend number. Otherwise, it is a factor of that number.
- Repeat the above three steps until we divide a number by the same number.

The above four steps may confuse you theoretically, but you can easily understand here by the following simple and understandable examples.

Let’s learn how to find the factors of number $3$.

The first natural number is $1$ in mathematics and let’s divide the number $3$ by $1$ firstly.

$3 \div 1$

$=\,\,$ $\dfrac{3}{1}$

Let’s use the long division method to divide the number $3$ by $1$.

$\require{enclose}

\begin{array}{rll}

3 && \hbox{} \\[-3pt]

1 \enclose{longdiv}{3}\kern-.2ex \\[-3pt]

\underline{-~~~3} && \longrightarrow && \hbox{$1 \times 3 = 3$} \\[-3pt]

\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}

\end{array}$

The remainder is zero, which means there is no remainder when the number $3$ is divided by $1$. It means, the number $1$ divides $3$ completely. Therefore, the number $1$ is called a factor of $3$.

The second natural number is $2$ and let’s repeat the same procedure to divide the number $3$ by $2$.

$3 \div 2$

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

Similarly, let’s use the long division method to divide the number $3$ by $2$.

$\require{enclose}

\begin{array}{rll}

1 && \hbox{} \\[-3pt]

2 \enclose{longdiv}{3}\kern-.2ex \\[-3pt]

\underline{-~~~2} && \longrightarrow && \hbox{$2 \times 1 = 2$} \\[-3pt]

\phantom{00} 1 && \longrightarrow && \hbox{Remainder}

\end{array}$

The remainder is one, which means there is a remainder when the number $3$ is divided by $2$. It means, the number $2$ does not divide $3$ completely. Therefore, the number $2$ is not a factor of $3$.

The third natural number is $3$ and let’s repeat the same process once again to divide the number $3$ by itself.

$3 \div 3$

$=\,\,$ $\dfrac{3}{3}$

Use the long division method to divide the number $3$ by itself.

$\require{enclose}

\begin{array}{rll}

1 && \hbox{} \\[-3pt]

3 \enclose{longdiv}{3}\kern-.2ex \\[-3pt]

\underline{-~~~3} && \longrightarrow && \hbox{$3 \times 1 = 3$} \\[-3pt]

\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}

\end{array}$

The remainder is zero, which means there is no remainder when the number $3$ is divided by the same number. It means, the number $3$ divides $3$ completely. Therefore, the number $3$ is called a factor of $3$.

The process of division should be stopped here because the natural numbers greater than $3$ are $4, 5, 6, \cdots$ and they cannot divide the number $3$ completely.

- There is no remainder when the numbers $1$ and $3$ divide the number $3$. It means, the numbers $1$ and $3$ divide the number $3$ completely. So, the numbers $1$ and $3$ are called the factors of $3$.
- There is a remainder when the number $2$ divides the number $3$. It means, the number $2$ does not divide the number $3$ completely. So, the number $2$ is not a factor of $3$.

In this way, the factors of every natural number can be found by factoring.

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