Math Doubts

What is a factor?

Definition

A quantity that multiplies another quantity is called a factor of their product.

Introduction

A quantity can be multiplied by another quantity and their product forms another quantity. Mathematically, each quantity that involves in the multiplication is called a factor of their product.

It is a basic concept, whereas it has significance in mathematics. If you are new to factors, you can easily know what a factor really is, by some simple arithmetic examples as follows. It helps you to use the concept of factors in higher mathematics.

Example: 1

$2 \times 3$

$\implies$ $2 \times 3$ $\,=\,$ $6$

In this example, $2$ and $3$ are two numbers and they are involved in multiplication. The product of numbers $2$ and $3$ is equal to $6$.

  1. The number $2$ is called a factor of $6$.
  2. The number $3$ is called a factor of $6$.

Therefore, the numbers $2$ and $3$ are called the factors of $6$.

Now, let’s look at another arithmetic example.

Example: 2

$4 \times 5 \times 7$

$\implies$ $4 \times 5 \times 7$ $\,=\,$ $140$

In this example, $4,$ $5$ and $7$ are numbers, involved in multiplication and their product is equal to $140$.

  1. The number $4$ is called a factor of $140$.
  2. The number $5$ is called a factor of $140$.
  3. The number $7$ is called a factor of $140$.

Therefore, the numbers $4,$ $5$ and $7$ are called the factors of $140$.

The above two examples cleared you to know what a factor is in mathematics. Now, let’s learn more about a factor further from the following example.

Example: 3

$3 \times 5$ $\,=\,$ $15$

According to above examples, you can easily say that the numbers $3$ and $5$ are factors of $15$. Yes, you are absolutely correct.

In other words, a number can be a factor of another number, if it divides another number completely. Let’s to prove it by dividing the number $15$ with $3$.

$\require{enclose}
\begin{array}{rll}
5 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{15}\kern-.2ex \\[-3pt]
\underline{-~~~15} && \longrightarrow && \hbox{$3 \times 5 = 15$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

There is no remainder when the number $3$ divides $15$, which means the number $3$ divides $15$ completely. So, the number $3$ is called a factor of $15$.

Similarly, it can be proved that the number $5$ is also a factor of $15$.

The fundamental definition of a factor and the above three simple examples helped you to understand the concept of a factor in mathematics.