Representation of factors

Definition

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

Introduction

The factors of a number are always finite but it can be quite difficult to express the factors of a number every time. Instead of writing the factors of a number, a system of denoting the factors of a quantity is required and it is called the representation of factors. It is also called the notation 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.

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