$1$ and $2$ are the factors of $2$.
The number two is a natural number and it is also a whole number. Mathematically, the number $2$ represents a whole quantity. The number $2$ should have to express as factors in some cases. So, it is essential for us to know the factors of two.
The factors of $2$ are $1$ and $2$ as per arithmetic and we should know why $1$ and $2$ are only factors of number $2$. So, let’s learn how to find the factors of $2$ in mathematics.
The number $1$ is a first natural number in mathematics. So, let’s divide the number $2$ by $1$ firstly.
$2 \div 1$
$=\,\,$ $\dfrac{2}{1}$
Use the long division method to divide the number $2$ by $1$ and it helps us to know about the remainder.
$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
1 \enclose{longdiv}{2}\kern-.2ex \\[-3pt]
\underline{-~~~2} && \longrightarrow && \hbox{$1 \times 2 = 2$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
There is no remainder when the number $2$ is divided by $1$, it clears that the number $1$ divides $2$ completely. Therefore, the number $1$ is a factor of $2$.
Now, let’s divide the number $2$ by itself.
$2 \div 2$
$=\,\,$ $\dfrac{11}{1}$
Let’s use long division method one more time to know whether the number $2$ divides itself completely or not.
$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
2 \enclose{longdiv}{2}\kern-.2ex \\[-3pt]
\underline{-~~~2} && \longrightarrow && \hbox{$2 \times 1 = 2$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
There is no remainder when the number $2$ is divided by itself, it means the number $2$ divides the same number completely. Therefore, the number $2$ is a factor of itself.
It is proved mathematically that the numbers $1$ and $2$ divide the number $2$ completely. So, the numbers $1$ and $2$ are the factors of $2$.
The factors of $2$ is expressed mathematically as follows.
$F_{2} \,=\, \{1, 2\}$
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