**Calculates the greatest common divisor of two integer numbers** without the need to perform the decomposition into prime factors of each of them. With our online calculator you can find the value of the GCD automatically:

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## What is the greatest common divisor?

The greatest common divisor or GCD of two or more numbers** is equal to the largest common integer** to all of them, which makes it possible to divide them all by their value.

Expressed in other words,** is the greatest common divisor** to all the numbers involved in the operation.

This is especially useful for simplify fractions and other operations, since **allows you to work with smaller numbers** and that makes the calculations much easier.

## How is the greatest common divisor calculated?

It is common practice to calculate the greatest common divisor of two or more numbers by calculating their** decomposition into prime factors**.

Once obtained, in order to obtain the GCD it is necessary to **multiplying the common values raised to the lowest exponent** as we can see below, taking as an example the numbers 48 and 60:

There are other methods to obtain the GCD, but this is undoubtedly the most widespread and it is also used for **finding the greatest common divisor of three numbers**.

As you can see much better with a solved example, we will calculate the **GCD of three issues** (24, 36, 40). To do this, the first thing we will do is to decompose it into prime factors:

24= 2 x 2 x 2 x 2 x 3 = 2

^{3}x 336 = 2 x 2 x 2 x 3 x 3 x 3 = 2

^{2}x 3^{3}40 = 2 x 2 x 2 x 2 x 2 x 5 = 2

^{3}x 5

Now we only have to select the factors common to the three numbers, paying attention to choose the ones with the lowest power or exponent:

GCD (24, 36, 40) = 2

^{2}= 4

**In the event that there is no common divisor, the following applies** to all the numbers, the result will be 1. This will happen if all the numbers are prime, for example.

Now that you know how to calculate the **greatest common divisor** If you have several numbers, you can use our online calculator to save time and avoid possible mistakes in the calculations. Remember that we also have a tool to obtain the least common multiple of two numbers.

## Greatest common divisor exercises

We will now look at several exercises in which we will calculate the **greatest common divisor of two numbers**.

### Greatest common divisor of 8 and 12

As we have seen in the first point, the first thing we have to do is to decompose each of the numbers into prime factors:

- 8 = 2 x 2 x 2 x 2 = 2
^{3} - 12: 2 x 2 x 2 x 3 = 2
^{2}x 3

Once we already have the numbers expressed as a multiplication of prime factors, we look at those that are common to both and always **we will keep those of lesser exponent** (2^{2}).

In this example, **the GCD of 8 and 12 equals 4**.

## How does the greatest common divisor calculator work?

Our **greatest common divisor calculator** has been developed to automate the above process.

This **saves you a lot of time and avoids errors** The calculator will factor the numbers for you, select the factors common to both numbers and multiply them correctly.

## Calculate the greatest common divisor in Excel

If you have Excel installed on your computer, you can also **calculate the GCD of multiple numbers** instantly.

To do this you simply have to open the spreadsheet program and type in an empty cell the following function:

=GCD(36,60,24)

In this example we have used the formula for **calculate the GCD of the numbers 36, 60 and 24**and 12 is the result.

Excel allows **calculating the greatest common divisor of two numbers** as a minimum, although if we wish, we can find the GCD of up to 255 values.

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