Arithmetic factors

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 $24$

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