A number is always divided by its each factor, which means a number is a factor of another number, when it divides another number completely. It clears that a factor of a number can be obtained by the division. So, let’s learn how to find the factors of every number mathematically.
There are three simple steps to find the factors of each number in mathematics.
The above three steps may confuse you theoretically, but you can easily understand here by the following simple arithmetic examples.
Let’s find the factors of $3$. There are two numbers $1$ and $2$ before the number $3$. So, the number $3$ should be divided by $1, 2$ and $3$ by the division method.
Firstly, let’s divide the number $3$ by the first natural number $1$.
$3 \div 1$
$=\,\,$ $\dfrac{3}{1}$
Use the Long division method to find the remainder when the number $3$ is divided 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 when the number $3$ is divided by $1$, which means there is no remainder and it proves that the number $1$ divides $3$ completely. So, the number $1$ is a factor of $3$.
The second natural number is $2$. So, let’s divide the number $3$ by the first natural number $2$.
$3 \div 2$
$=\,\,$ $\dfrac{3}{2}$
Use the long division method to find the remainder when the number $3$ is divided 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 $3$. So, let’s divide the number $3$ by itself.
$3 \div 3$
$=\,\,$ $\dfrac{3}{3}$
Use the long division method to find the remainder when the number $3$ is divided by the same number.
$\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}$
There is no remainder when the real number $3$ is divided by itself. So, it is proved that the number $3$ is a factor of itself.
Now, the process of division should be stopped here because the numbers greater than $3$ are $4, 5, 6, \cdots$ They cannot divide the number $3$ completely.
This simple example helped you to understand the process of finding the factors of a number in mathematics. You can now use this procedure to find the factors of any number easily.
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