$1,$ $2$ and $4$ are the factors of $4$.
The number four is a natural number and also a whole number. The number $4$ represents a whole quantity in mathematics and it should be expressed as factors in some cases. Therefore, it is must for us to know what the factors of four are, and let’s learn how to find the factors of $4$ arithmetically.
Arithmetically, let’s learn why $1, 2$ and $4$ are only factors of the number $4$.
Let’s divide the number $4$ by the first natural number $1$.
$4 \div 1$
$=\,\,$ $\dfrac{4}{1}$
Divide the number $4$ by $1$ with long division method to find the remainder.
$\require{enclose}
\begin{array}{rll}
4 && \hbox{} \\[-3pt]
1 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$1 \times 4 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
When the number $4$ is divided by $1$, there is no remainder and it proves that the number $1$ divides $4$ completely. Therefore, the number $1$ is a factor of $4$.
Let’s divide the number $4$ by the second natural number $2$.
$4 \div 2$
$=\,\,$ $\dfrac{4}{2}$
Divide the number $4$ by $2$ with long division method to find the remainder.
$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
2 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$2 \times 2 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
When the number $2$ divides $4$, there is no remainder and it proved that the number $2$ divides $4$ completely. Therefore, the number $2$ is a factor of $4$.
Now, let’s divide the number $4$ by the third natural number $3$.
$4 \div 3$
$=\,\,$ $\dfrac{4}{3}$
Divide the number $4$ by $3$ with long division method to find the remainder.
$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~3} && \longrightarrow && \hbox{$3 \times 1 = 3$} \\[-3pt]
\phantom{00} 1 && \longrightarrow && \hbox{Remainder}
\end{array}$
When the number $4$ is divided by $3$, there is a remainder and it proves that the number $3$ does not divide $4$ completely. Therefore, the number $3$ is not a factor of $4$.
Finally, let’s divide the number $4$ by the same number.
$4 \div 4$
$=\,\,$ $\dfrac{4}{4}$
Divide the number $4$ by itself with long division method to find the remainder.
$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
4 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$4 \times 1 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
When the number $4$ divides the same number, there is no remainder and it proved that the number $4$ divides itself completely. Therefore, the number $4$ is a factor of itself.
It proved that the numbers $1,$ $2$ and $4$ divide the number $4$ completely but the number $3$ cannot divide $4$ completely. So, the numbers $1,$ $2$ and $4$ are factors of number $4$ mathematically.
The number $4$ can be written in its factors form possibly as follows.
$(1).\,\,$ $4 \,=\, 1 \times 4$
$(2).\,\,$ $4 \,=\, 2 \times 2$
The factors of $4$ can be represented in set form mathematically as follows.
$F_{4} \,=\, \{1, 2, 4\}$
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