# gcd calculation online

## Calculus gcd

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### Function : gcd

#### Summary :

GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.

gcd online

# Calculation of the greatest common divisor of two integers (GCD)

## Definition of the GCD

In arithmetic, the largest divisor that two integers have in common is called the GCD (Greatest Common Divisor) or the GCF (Greatest Common Factor).

## Calculating the GCD

The GCD calculator allows to calculate online the largest common divisor of two integers. To calculate the GCD online of two integers, the calculator uses Euclid's algorithm. The steps for calculating the GCD are specified.

Thus, for calculating the online gcd of two integers 150 and 350 , just type gcd(150;350) , the calculator returns the result 50.

The calculation of the GCD is particularly useful for simplifying a fraction and put in the form of an irreducible fraction.

## Principle of the Euclidean algorithm

The Euclidean algorithm uses successive Euclidean division to determine the GCD. To calculate the greatest common divisor of two integers a and b, using the algorithm is performed the Euclidean division of a by b , we obtain a = bq + r. If r is zero, q is the GCD , otherwise it repeats the operation by performing the Euclidean division of b and r .The algorithm uses the following property gcd (a,b)= gcd(b,r). The GCD is the last non-zero remainder . The following example shows a detailed calculation using the algorithm of Euclide to determine the GCD of two numbers.

GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.

#### Syntax :

gcd(a;b), a and b are integers.

#### Examples :

gcd(15;25), returns 5

Calculate online with gcd (gcd calculation online)