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.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2025 Math Doubts, All Rights Reserved