GCD Calculator

GCD Formula:

Euclidean Algorithm
While n mod m is not equal to 0
n = m
m = n mod m

Then GCD = m

GCD Definition

Use our free Greatest Common Divisor (GCD) calculator and get your answers in an instant! When looking for the (GCD), it is important to consider the numbers in question. If one will divide evenly by the other, that is likely the number you are seeking. However, that might not be true. This calculator will tell you what the answer is so you can check it against the results you come up with. If you do it by hand, you might end up using a trial-by-error method when comparing the two values’ prime numbers.

The GCD is used in a variety of applications. Probably one of the easiest to identify is creating an equal division of one value with the other. For instance, 8 buns and 10 hot dogs gives you a GCD of 2. Using this number, you can calculate how many packages of buns and hot dogs you need to have an equal number of each.

What the Calculator Does

Here is how it works:

A. Number 1 is the first quantity
B. Number 2 is the second quantity
C. When you click calculate, the program returns the GCD

Use the GCD to multiply both numbers until you end up with the same value if you are looking for an equal number.

Putting the Greatest Common Divisor to Use

The GCD is probably used most for comparing the common values shared between two numbers. For instance, 30 and 7 have the number 1 in common. While not all GCD’s will be expressed as prime numbers, they are products of prime numbers.

The prime numbers of 30 are 1, 2, 3, and 5; those of 6 are 1, 2, and 3. The common numbers between them (1, 2, and 3) multiple to 6, which makes 6 the GCD.

Using the above method to calculate the GCD is known as prime factoring. Unless you are using a calculator, this is probably the easiest way to find the GCD if the values do not immediately suggest a common value between them. That can take time with larger values, so this calculator will help you save time.

How to Calculate GCD

Let's be honest - sometimes the best gcd calculator is the one that is easy to use and doesn't require us to even know what the gcd formula is in the first place! But if you want to know the exact formula for calculating gcd then please check out the "Formula" box above.

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