gcd algorithm

The Greatest Common Divisor (GCD) algorithm in C++ is used to find the largest positive integer that divides two given integers without leaving a remainder. Here is an explanation of each step involved in the GCD algorithm:

1. Start by defining two integers, let's say "a" and "b", for which we want to find the GCD.
2. Check if either "a" or "b" is equal to zero. If either of them is zero, return the other number as the GCD since any number divides zero.
3. If both "a" and "b" are non-zero, proceed to the next step.
4. Use the modulo operator (%) to find the remainder of dividing "a" by "b". Assign this value to a temporary variable, let's call it "temp".
5. Check if "temp" is equal to zero. If it is, return the value of "b" as the GCD since "b" divides "a" without leaving a remainder.
6. If "temp" is not equal to zero, assign the value of "b" to "a" and the value of "temp" to "b".
7. Repeat steps 4-6 until "temp" becomes zero.
8. Once "temp" becomes zero, return the value of "b" as the GCD of the original "a" and "b".

This algorithm works because at each step, we are reducing the problem by finding the remainder of the division and swapping the values. Eventually, we will reach a point where the remainder is zero, indicating that we have found the GCD.