# Common factor Method

## Definition

A method of finding the greatest divisor or highest factor from the common factors of the given numbers is called the common factor method.

### Introduction

The numbers are factored in mathematics to write every number as a product of two or more factors. In some cases, one or more factors may be commonly appeared in them and they are called common factors. Identifying the greatest or highest common factor (H.C.F) in them is called the common factor method.

There are three simple steps to find the greatest common divisor (G.C.D).

1. Find all the possible factors of each given number.
2. Identify the common factors by comparing the factors of the given numbers.
3. Identify the greatest or highest factor in the common factors to find the greatest common divisor or highest common factor of the given numbers.

Now, let’s learn how to use the common factor method to find the greatest common factor (G.C.F) mathematically.

#### Example

Firstly, find the factors of the numbers $16$ and $24$.

$F_{16}$ $\,=\,$ $\big\{1,\, 2,\, 4,\, 8,\, 16\big\}$

$F_{24}$ $\,=\,$ $\big\{1,\, 2,\, 3,\, 4,\, 6,\, 8,\, 12,\, 24\big\}$

Now, compare the factors of the numbers $16$ and $24$ to find the common factors. We can observe that $1,$ $2,$ $4$ and $8$ are commonly appeared in their factors.

The number $8$ is the greatest or highest number in the common factors $1,$ $2,$ $4$ and $8$. Therefore, the number $8$ is called the greatest common divisor or highest common factor.

The greatest common divisor or highest common factor or greatest common factor of the numbers $16$ and $24$ are written in mathematics as follows.

1. $\gcd(16,\,24) \,=\, 8$
2. $\operatorname{hcf}(16,\,24) \,=\, 8$
3. $\operatorname{gcf}(16,\,24) \,=\, 8$

#### Worksheet

The list of common factor method questions for practices with solutions to learn how to find the greatest common divisor or the highest common factor of the given numbers.

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