**Instructions:**

- Enter your numbers separated by commas.
- Click "Calculate" to find the common factors.
- View the chart representation of the common factors below.
- Copy the results to the clipboard if needed.
- Check the calculation history for previous calculations.
- Click "Clear Results" to reset the results and chart.

**Calculation History:**

A common factors calculator is a tool that allows users to calculate the common factors of two or more numbers. Common factors are numbers that can divide into each given number without leaving a remainder.

## Concepts

The following are some of the key concepts that underlie common factors calculators:

- Factor: A factor of a number is a number that can divide into that number without leaving a remainder.
- Common factor: A common factor of two or more numbers is a number that can divide into each of the given numbers without leaving a remainder.
- Greatest common factor (GCD): The greatest common factor (GCD) of two or more numbers is the largest number that can divide into each given number without leaving a remainder.

## Formulae

The following formula is used to calculate the greatest common factor (GCD) of two numbers:

```
GCD (a, b) = max {x | x is a factor of a and b}
```

where:

`a`

and`b`

are the two numbers to calculate the GCD for.

Several different algorithms can be used to calculate the GCD of two numbers. One common algorithm is the Euclidean algorithm.

## Benefits

There are several benefits to using a common factors calculator, including:

- Accuracy: Common factors calculators are very accurate, as they use sophisticated mathematical algorithms to perform their calculations.
- Convenience: Common factors calculators can save users a lot of time and effort, as they can perform complex calculations quickly and easily.
- Flexibility: Common factors calculators can calculate the common factors of any two or more numbers, regardless of their size or complexity.
- Versatility: Common factors calculators can be used in a variety of fields, including mathematics, engineering, and computer science.

## Interesting facts about common factors

- The common factors of two numbers are always less than or equal to the smaller of the two numbers.
- The greatest common factor (GCD) of two numbers is always a multiple of the least common multiple (LCM) of the two numbers.
- The common factors of a prime number are only 1 and itself.

## Use Cases

Common factors calculators can be used in various fields such as:

- Mathematics: To find out the greatest common divisor (GCD) between two or more integers.
- Engineering: To find out the greatest common divisor (GCD) between two or more integers which helps simplify fractions.
- Computer Science: To find out if two integers are coprime or not.

**References**

Here are some references related to this topic:

- David Halliday, Robert Resnick, and Jearl Walker: Fundamentals of Physics, 11th Edition
- Paul A. Tipler and Gene Mosca: Physics for Scientists and Engineers, Volume 1: Mechanics, Oscillations and Waves, Thermodynamics, 7th Edition
- Raymond A. Serway and John W. Jewett: Physics for Scientists and Engineers, Volume 1: Mechanics, 10th Edition