What are the Factors of 3?
Factors
$1$ and $3$ are the factors of $3$.
The number three is a natural number and also a whole number. Mathematically, the number $3$ represents a whole quantity and it should be expressed as factors in some cases in mathematics. So, it is most important for us to know the factors of three.
According to arithmetic, the factors of three are $1$ and $3$. We must know why $1$ and $3$ are only factors of number $3$. Therefore, let’s learn how to find the factors of $3$ mathematically.
In mathematics, the number $1$ is a first natural number. So, let’s divide the number $3$ firstly by $1$.
Step: 1
$3 \div 1$
$=\,\,$ $\dfrac{3}{1}$
Let’s divide the number $3$ by $1$ with long division method to know about the remainder.
$\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 clears that the number $1$ divides $3$ completely. So, the number $1$ is a factor of $3$.
Similarly, let’s divide the number $3$ by $2$.
Step: 2
$3 \div 2$
$=\,\,$ $\dfrac{3}{2}$
Let’s divide the number $3$ by $2$ with the long division method to know about the remainder.
$\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 $1$ when the number $3$ is divided by $2$. It means the number $2$ does not divide $3$ completely. So, the number $2$ is not a factor of $3$.
Similarly, let’s divide the number $3$ by itself.
Step: 3
$3 \div 3$
$=\,\,$ $\dfrac{3}{3}$
Once again, let’s use the long division method to divide the number $3$ by itself and it helps us to know about the remainder.
$\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 number $3$ is divided by itself. It is proved that the number $3$ divides same number completely. So, the number $3$ is a factor of itself.
Conclusion
It has proved mathematically that the numbers $1$ and $3$ divide the number $3$ completely. Therefore, the numbers $1$ and $3$ are the factors of $3$.
Factorization
The factors of $3$ are $1$ and $3$. So, the number $3$ can be expressed in terms of its factors $1$ and $3$ as follows.
$3 \,=\, 1 \times 3$
Representation
The factors of $3$ is expressed in mathematics as follows.
$F_{3} \,=\, \{1, 3\}$