Math Doubts

What is a factor?

Definition

A whole number that divides the given number exactly, without leaving any remainder is called a factor.

Introduction

A factor is a fundamental concept in mathematics. It helps us understand the properties of numbers, such as divisibility, and how numbers relate to each other.

what is a factor in math with examples, student learning factors of whole numbers in a classroom

Examples of factors

Let’s begin by learning what a factor really is, with some simple numerical examples of factors.

Example

$6 \div 2$

The numbers $2$ and $6$ are both whole numbers. Now, divide $6$ by $2$ to see if there is any remainder.

$\require{enclose}
\begin{array}{rll}
3 && \hbox{} \\[-3pt]
2 \enclose{longdiv}{~6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$2 \times 3 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

When $6$ is divided by $2$, there is no remainder. This means that $2$ divides $6$ exactly, so $2$ is called a factor of $6$.

This simple numerical example demonstrates that a whole number that divides a given number exactly, without leaving any remainder, is called a factor of that number.

Now, let’s consider another arithmetic example to understand the concept of a factor more clearly.

Example

$6 \div 3$

The numbers $3$ and $6$ are both whole numbers. Next, divide $6$ by $3$ to see if there is a remainder.

$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{~6}\kern-.2ex \\[-3pt]
\underline{-~~~6} && \longrightarrow && \hbox{$3 \times 2 = 6$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

Dividing $6$ by $3$ leaves no remainder. This shows that $3$ divides $6$ exactly, so $3$ is a factor of $6$.

These arithmetic examples illustrate the divisibility property of numbers and show how to find all factors of a number, helping beginners understand what a factor is and how factors work in math.

The above examples show that $2$ and $3$ are factors of the number $6$. Multiplying these factors gives $6$, which demonstrates the relationship between the factors of a number.

Example

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

Factors of a number have a mutual relationship, which means that certain factors can be multiplied together to produce the original number, and it helps beginners understand how factors work in math.

Finally, let’s consider one more simple example to understand the concept of a factor more clearly.

Example

$6 \div 5$

The numbers $5$ and $6$ are both whole numbers. Now, divide $6$ by $5$ to determine whether there is a remainder.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
5 \enclose{longdiv}{~6}\kern-.2ex \\[-3pt]
\underline{-~~~5} && \longrightarrow && \hbox{$5 \times 1 = 5$} \\[-3pt]
\phantom{00} 1 && \longrightarrow && \hbox{Remainder}
\end{array}$

When $6$ is divided by $5$, the remainder is $1$. This shows that $5$ does not divide $6$ exactly, so $5$ is not a factor of $6$.

Based on the examples of factors, you have clearly learned what a factor of a number is.

Important Points About Factors

Now, let’s now look at some key points to remember.

  1. Factors are always whole numbers.
  2. A number can have more than one factor.
  3. Factors help us understand division, multiplication, and how numbers relate to each other.