The GCD (Greatest Common Divisor) of 2 or more integers is the largest positive integer. Also, this +ve interger must divides each of the input integers completly without leaving any remainder. Here, is an example, the GCD of 8 and 12 is 4 as 4 the maximum number which divides fully both 8 or 12.
Moreover, GCD is crucial in numerous mathematical calculations, such as Reducing fractions, Diophantine equations and Cryptography.
How to Calculate GCD?
We can find the GCD of two numbers in many ways:
Prime Factorization: Find the product of the common prime multipart as when moving from littlest to the biggest.
Euclidean algorithm: A more efficient way of calculating GCD based on the principle that the GCD of two numbers is also a divisor of their difference.
The Euclidean Algorithm is like the following:
- You are given two numbers a and b where a > b, replace a with a % b.
- Do this in a loop until b=0.
- This answer will be the GCD of the original two numbers.
GCD Calculator
Greatest Common Divisor (GCD), also known as Greatest Common Factor (GCF) or Highest Common Factor (HCF), is usually the largest positive integer that can divide two or more integers without giving a remainder.
This calculator figure out the GCD of two or more positive integers using the Euclidean Algorithm, showing each calculation step for better comprehension!