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

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

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.

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.

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

See also

- Number of arrangement of a set calculator : arrangement. To calculate online the number of arrangement of p elements of a set of n elements.
- Calculation of binomial coefficients : binomial_coefficient. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- To count the number of combinations : combination. To calculate the number of k elements of part of a set of n elements.
- Base-n converter : base_converter. The calculator allows you to make decimal, binary, hexadecimal conversions, and more generally to any base n between 2 and 36.
- Prime factorization calculator : prime_factorization. The function prime_factorization is used to calculate online the decomposition of an integer into prime factors.
- Quotient and remainder calculator : euclidean_division. The calculator allows to find online the quotient and the remainder in the euclidean division of two polynomials or two integers.
- Parity of a number : is_odd. Is_odd function returns true if the number passed is odd, false otherwise.
- Parity of a number : is_even. Is_even function returns 1 if the number is even, 0 otherwise.
- Factorial calculator : factorial. The factorial of a natural number n is the product of the positive integers less than or equal to n. The factorial calculator allows you to find this number.
- Integer calculations : integer_functions. This calculator allows you to apply special functions to an integer: prime_factorization, base_converter, factorial, percentage, permutation, perimeter, is_even, is_odd.
- Permutation calculator : permutation. To calculate online the number of permutation of a set of n elements.
- Gcd calculation online : gcd. GCD calculator that uses Euclid's algorithm to give the steps of the GCD calculation.
- Least common multiple : lcm. LCM calculator to calculate the least common multiple (LCM).
- Pythagorean theorem calculator : pythagorean. The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.
- Countdown solver : arithmetic_solver. This countdown solver allows finding a target number from a set of integer in using arithmetic operations.