What are Factor Pairs?
Fact-checked: February 22, 2026
Definition
Two non-zero integers whose product equals a given number are called a pair of factors.
Introduction to the Pair of factors
In arithmetic, understanding how numbers are formed and how they can be broken down is essential. One important concept is factor pairs, which help explain how a number is built through multiplication.
A factor pair consists of two numbers that multiply together to give a specific number. In other words, if two numbers are multiplied and their product equals a given number, those two numbers are called the factors of that number. When taken together as a set of two, they form a factor pair.
Example
$2 \times 5 \,=\, 10$
The numbers $2$ and $5$ are two factors of $10$. Together, they form a factor pair of $10$.
How to Represent a Factor Pair
A factor pair is written using parentheses to show the two factors together as a set. The numbers are separated by a comma and enclosed within parentheses. So, an ordered pair notation is used to denote the factor pairs in mathematics.
For example, the factor pair of $10$ is written as $(2, 5)$.
This format resembles ordered pair notation in mathematics. However, in a factor pair, the order of the numbers does not change the product.
Example
$5 \times 5 \,=\, 25$
In this case, the number $5$ is a factor of $25$, and it is multiplied by itself to obtain the given number. So, the factor pair of $25$ is written as $(5, 5)$.
Let’s understand how to write a factor pair of a number in mathematical notation by looking at another example.
The factors of $10$ are $1$, $2$, $5$, and $10$, and the corresponding negative factors are $−1$, $−2$, $−5$, and $−10$.
- Since $1 \times 10$ $\,=\,$ $10$, a factor pair of $10$ is $(1, 10)$.
- Since $2 \times 5$ $\,=\,$ $10$, a factor pair of $10$ is $(2, 5)$.
Therefore, the pairs of positive factors of $10$ are written as $(1, 10)$ and $(2, 5)$
- Since $(-1) \times (-10)$ $\,=\,$ $10$, a factor pair of $10$ is $(-1, -10)$.
- Since $(-2) \times (-5)$ $\,=\,$ $10$, a factor pair of $10$ is $(-2, -5)$.
Therefore, the pairs of negative factors of $10$ are written as $(-1, -10)$ and $(-2, -5)$
The pairs of factors of $10$ is written as $(-1, -10)$, $(-2, -5)$, $(1, 10)$ and $(2, 5)$. In this way, you can write the factor pair of any number in ordered pair notation to represent it clearly in mathematics.
