The factors of $12$ are $1, 2, 3, 4, 6$ and $12$.
The number $12$ is a natural number and it represents a whole quantity.
Now, let’s learn how to find the factors of twelve mathematically by factoring the number $12$ and it proves why $1, 2, 3, 4, 6$ and $12$ are factors of $12$.
Let’s divide the number $12$ by $1$ firstly.
$12 \div 1$
$=\,\,$ $\dfrac{12}{1}$
$=\,\,$ $12$
The number $1$ divides $12$ completely. So, the number $1$ is a factor of $12$.
Now, let’s divide the number $12$ by $2$.
$12 \div 2$
$=\,\,$ $\dfrac{12}{2}$
$=\,\,$ $6$
The number $2$ divides $12$ completely. Therefore, the number $2$ is a factor of $12$.
Similarly, let’s divide the number $12$ by $3$.
$12 \div 3$
$=\,\,$ $\dfrac{12}{3}$
$=\,\,$ $4$
The number $3$ divides $12$ completely. So, the number $3$ is a factor of $12$.
In the same way, let’s divide the number $12$ by $4$.
$12 \div 4$
$=\,\,$ $\dfrac{12}{4}$
$=\,\,$ $3$
The number $4$ divides $12$ completely. Therefore, the number $4$ is a factor of $12$.
Similarly, let’s divide the number $12$ by $5$.
$12 \div 5$
$=\,\,$ $\dfrac{12}{5}$
Let’s observe the division process of natural number $12$ by $5$.
$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
5 \enclose{longdiv}{12}\kern-.2ex \\[-3pt]
\underline{-~~~10} && \longrightarrow && \hbox{$5 \times 2 = 10$} \\[-3pt]
\phantom{00} 2 && \longrightarrow && \hbox{Remainder}
\end{array}$
There is a remainder in the division and it expresses that the number $5$ cannot divide $12$ completely. So, the number $5$ is not a factor of $12$.
Now, let’s divide the number $12$ by $6$.
$12 \div 6$
$=\,\,$ $\dfrac{12}{6}$
$=\,\,$ $2$
The number $6$ divides $12$ completely. Therefore, the number $6$ is a factor of $12$.
Let’s try to divide the number $12$ by the numbers $7, 8, 9, 10$ and $11$.
$(1).\,\,$ $12 \div 7$ $\,=\,$ $\dfrac{12}{7}$ $\,=\,$ $1.7142\cdots$
$(2).\,\,$ $12 \div 8$ $\,=\,$ $\dfrac{12}{8}$ $\,=\,$ $1.5$
$(3).\,\,$ $12 \div 9$ $\,=\,$ $\dfrac{12}{9}$ $\,=\,$ $1.3333\cdots$
$(4).\,\,$ $12 \div 10$ $\,=\,$ $\dfrac{12}{10}$ $\,=\,$ $1.2$
$(5).\,\,$ $12 \div 11$ $\,=\,$ $\dfrac{12}{11}$ $\,=\,$ $1.0909\cdots$
The numbers $7, 8, 9, 10$ and $11$ are failed to divide $12$ completely. So, the numbers from $7$ to $11$ are not factors of $12$.
Finally, let’s divide the number $12$ by the same number.
$12 \div 12$
$=\,\,$ $\dfrac{12}{12}$
$=\,\,$ $1$
The factorization of $12$ is proved that the whole numbers $1, 2, 3, 4, 6$ and $12$ divided the number $12$ completely. So, the numbers $1, 2, 3, 4, 6$ and $12$ are called the factors of $12$.
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