Factors of 2
Definition
A non-zero integer that divides $2$ exactly without leaving any remainder is called a factor of $2$.
Introduction to the Factors of 2
A factor of $2$ is an integer that divides $2$ exactly with no remainder. Integers include both positive and negative whole numbers. Although $0$ is an integer, it cannot divide $2$, so it is excluded when finding the factors of $2$. Therefore, only non-zero integers that divide $2$ exactly are factors of $2$.
What are the Factors of 2?
Mathematically, the non-zero integers $1$ and $2$ divide the number $2$ exactly without leaving any remainder. Hence, the factors of $2$ are $1$ and $2$. For every positive factor of $2$, there is a corresponding negative factor. Here is the list of factors of $2$ with both positive and negative signs.
- The positive factors of $2$ are $1$ and $2$.
- The negative factors of $2$ are $-1$ and $-2$.
How to Find the Factors of 2
Now, let’s learn how to find the factors of $2$ mathematically.
Example
$2 \div 1$
The number $2$ is a whole number and a positive integer. Similarly, the number $1$ is also a whole number and a positive integer. Now, divide $2$ by $1$ to check whether there is any 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 $1$, which means that $1$ divides $2$ exactly. Therefore, $1$ is a factor of $2$.
Example
$2 \div 2$
The number $2$ is a whole number and a non-zero positive integer. Now, let us divide $2$ by itself to check whether there is any remainder.
$\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}$
When the number $2$ is divided by itself, there is no remainder, which means that $2$ divides itself exactly. Therefore, the positive integer $2$ is a factor of itself.
The next positive integer after $2$ is $3$, but $3$ does not divide $2$ exactly because it is greater than $2$.
What are the Negative Factors of 2?
The positive factors of $2$ are $1$ and $2$, and the corresponding negative factors are $-1$ and $-2$.
What are the Factor Pairs of 2?
Now, let’s discuss both the positive and negative factor pairs of $2$.
- The positive factor pair of the number $2$ is $(1, 2)$.
- The negative factor pair of the number $2$ is $(-1, -2)$.
How to Factorize 2
The number $2$ can be expressed in two ways as a product of its factors using factor pairs.
- $2$ $\,=\,$ $1 \times 2$
- $2$ $\,=\,$ $(-1) \times (-2)$
Representation of Factors of 2
The factors of $2$, including both positive and negative integers, can be written in set notation as follows
$F_2 = \{-2, -1, 1, 2\}$
