Representation of factors

Definition

The system of denoting the factors of a quantity is called the representation of the factors.

Introduction

The number of factors of every natural number are finite. So, it is possible to express all of them in mathematical form. However, it is essential to create a system of expressing the factors of a number in mathematics and it is called the representation of factors.

Representation

There are two ways to express the factors of a number mathematically but you must know how to find the factors of a number firstly in arithmetic.

The word “factors” is denoted by the uppercase alphabet $F$. So, the factors a number is simply written as $F$ subscript that number. For example, the factors of $18$ is simply written as $F_{18}$ in mathematics.

Now, let’s learn how to represent the factors of a number mathematically in both methods.

Basic form

The factors of $18$ are written as $1$, $2$, $3$, $6$, $9$ and $18$ in elementary mathematics.

In elementary level, the factors of a number are written in a row but a comma symbol with some space between the factors are included for separating every two factors but the word “and” is written between the last two factors.

Therefore, the factors of a number are written as follows by considering the theory of elementary mathematics.

$F_{18}$ $\,=\,$ $1$, $2$, $3$, $6$, $9$ and $18$

Set form

The factors of a number are also a set. So, the factors of a number can be expressed in roster notation as per set theory. Therefore, the factors of $18$ is simply written in mathematics as follows.

$F_{18}$ $\,=\,$ $\{1, 2, 3, 6, 9, 18\}$

In this general form, all factors are in horizontal path by separating every two factors with a comma symbol and some space, and the curly brackets denote the collection of factors of that number.

In this way, the factors of a number can be represented mathematically and you can follow any of the above two methods in mathematics.

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.