GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.
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
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
Principle of the Euclidean algorithm
The Euclidean algorithm uses successive
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.
Quiz on GCD
The site proposes
quizzes on the GCD
, which allow to deepen the techniques of calculation with the numbers and the simplification of fraction.
gcd(a;b), a and b are integers.
gcd(15;25), returns 5
Calculate online with gcd (gcd calculation online)