Factors of 6

The factors of $6$ are $1$, $2$, $3$, and $6$.

What are the factors of 6?

A whole number that divides $6$ exactly is called a factor of $6$.

In mathematics, the factors of the number $6$ can be found by dividing it by each whole number. If a whole number divides $6$ completely, meaning there is no remainder, then that whole number is called a factor of $6$.

How to Find the Factors of 6

To find the factors of $6$, we divide the number $6$ by whole numbers starting from $1$. Let us divide $6$ by the whole numbers $1$, $2$, $3$, $4$, $5$, and $6$ to check whether the remainder is zero.

$6 \div 1$

Divide the number $6$ by $1$ to check whether $1$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
6 && \hbox{} \\[-3pt]
1 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$1 \times 6 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

The remainder is zero when the number $6$ is divided by $1$, which means that $1$ divides $6$ completely. Therefore, $1$ is a factor of $6$.

$6 \div 2$

Divide the number $6$ by $2$ to check whether $2$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
3 && \hbox{} \\[-3pt]
2 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$2 \times 3 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

There is no remainder when the number $6$ is divided by $2$, which means that $2$ divides $6$ completely. Therefore, $2$ is a factor of $6$.

$6 \div 3$

Divide the number $6$ by $3$ to check whether $3$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$3 \times 2 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

The remainder is zero when the number $6$ is divided by $3$, which means that $3$ divides $6$ completely. Therefore, $3$ is a factor of $6$.

$6 \div 4$

Divide the number $6$ by $4$ to check whether $4$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
4 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$4 \times 1 = 4$} \\[-3pt]
\phantom{00} 2 && \longrightarrow && \hbox{Remainder}
\end{array}$

The remainder is $2$ when the number $6$ is divided by $4$, which means that $4$ cannot divide $6$ completely. Therefore, $4$ is not a factor of $6$.

$6 \div 5$

Divide the number $6$ by $5$ to check whether $5$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
5 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~5} && \longrightarrow && \hbox{$5 \times 1 = 5$} \\[-3pt]
\phantom{00} 1 && \longrightarrow && \hbox{Remainder}
\end{array}$

The remainder is $1$ when the number $6$ is divided by $5$, which means that $5$ cannot divide $6$ completely. Therefore, $5$ is not a factor of $6$.

$6 \div 6$

Divide the number $6$ by itself to check whether $6$ divides $6$ without leaving a remainder.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
6 \enclose{longdiv}{6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$6 \times 1 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

Although the numbers $1$ through $6$ can be used as divisors, only $1$, $2$, $3$, and $6$ divide $6$ exactly without leaving a remainder. Therefore, the factors of $6$ are $1$, $2$, $3$, and $6$.