Factors of 3
Definition
A non-zero integer that divides $3$ exactly without leaving any remainder is called a factor of $3$.
Introduction to the Factors of 3
A factor of $3$ is a non-zero integer that divides $3$ exactly without leaving a remainder. Integers include both positive and negative whole numbers. Although $0$ is an integer, it cannot divide $3$, so it is not considered a factor of $3$. Therefore, only non-zero integers that divide $3$ exactly are called factors of $3$.
What are the Factors of 3?
The non-zero integers $1$ and $3$ divide the number $2$ exactly without leaving any remainder. Hence, the factors of $3$ are $1$ and $3$ mathematically. For every positive factor of $3$, there is a corresponding negative factor. Here is the list of factors of $3$ with both positive and negative signs.
- The positive factors of $3$ are $1$ and $3$.
- The negative factors of $3$ are $-1$ and $-3$.
How to Find the Factors of 3
Now, let’s learn how to find the factors of $3$ mathematically.
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.
$F_{3} \,=\, \{1, 3\}$
