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gcd using euclids algorithm

GCD stands for greatest common divisor. GCD of two numbers is the greatest number that divides both numbers without leaving a remainder. Euclidean algorithm for finding the gcd is based on the principle that the gcd of two numbers does not change if the larger number is replaced by its difference with the smaller number.
Let us consider the example of 206 and 40, we find that 2 is the gcd of 206 and 40 also according to the above statement the gcd of 166 (206 - 40) and 40 is also 2.

 To know more about GCD click here.

 In the below program we follow the below steps
  • Step 1: In each iteration calculate the quotient 
  • Step 2: Then subtract the product of quotient and the smaller number from the bigger number
  • Step 3: Replace the bigger number by the remainder. 
  • Step 4: Repeat above steps until the smaller number becomes 0


GCD using euclids algorithm




C++ Program

Sample input and output to check the program




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