Gcd calculation online : How to use it?
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
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.
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.
- 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.
- Factoring calculator : factor. The factoring calculator allows to factor an algebraic expression online with steps.
- 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.