Math Doubts

Factors in Arithmetic form

Introduction

Any quantity can be divided as the product of two or more quantities and each quantity is multiplying another quantity in the product for representing the actual quantity. Each multiplying quantity is called as a factor in mathematics.

For example, $6$ is a quantity and try to express it as product of two or more quantities.

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

The quantity $6$ is divided as product of two quantities $2$ and $3$. They both are multiplying each other to represent the actual quantity $6$. Therefore, the numbers $2$ and $3$ are called as factors.

A factor can successfully divide the quantity.

$\implies$ $\dfrac{6}{2} \,=\, 3$

In this case, the number $2$ divides the number $6$ completely. So, the number $2$ is called as a factor of $6$. Similarly, the quotient of them is also a factor. So, the quotient $3$ is also called as a factor of $6$ because it can also divide the number $6$.

$\implies$ $\dfrac{6}{3} \,=\, 2$

Example

$24$ is a number and try to express it as product of two or more numbers in possible ways.

$(1) \,\,\,\,\,\,$ $24$ $\,=\,$ $1 \times 24$
The numbers $1$ and $24$ are factors of $24$.

$(2) \,\,\,\,\,\,$ $24$ $\,=\,$ $1 \times 2 \times 12$
The numbers $1$, $2$ and $12$ are called factors of $24$.

$(3) \,\,\,\,\,\,$ $24$ $\,=\,$ $1 \times 2 \times 3 \times 4$
The numbers $1$, $2$, $3$ and $4$ are called factors of $24$.

$(4) \,\,\,\,\,\,$ $24$ $\,=\,$ $2 \times 3 \times 4$
The numbers $2$, $3$ and $4$ are called factors of $24$.

$(5) \,\,\,\,\,\,$ $24$ $\,=\,$ $2 \times 12$
The numbers $2$ and $12$ are called factors of $24$.

$(6) \,\,\,\,\,\,$ $24$ $\,=\,$ $3 \times 8$
The numbers $3$ and $8$ are called factors of $24$.

$(7) \,\,\,\,\,\,$ $24$ $\,=\,$ $4 \times 6$
The numbers $4$ and $6$ are called factors of $24$.

The quantity $24$ is divisible by the numbers $1$, $2$, $3$, $4$, $6$, $8$, $12$ and $24$. Therefore, they are called as factors of $24$.

Representation

In mathematics, the factor of a quantity can be written in short form. For example, the factors of $24$ is written as $F$ subscript $24$.

${F}_{24}$ $\,=\,$ $1$, $2$, $3$, $4$, $6$, $8$, $12$ and $24$

Problems

Learn how to find the factors of any number with understandable steps

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 - 2023 Math Doubts, All Rights Reserved