

The algorithm you described is similar to the Euclidean algorithm for finding the greatest common divisor (GCD) of two natural numbers. The Euclidean algorithm is a well-known and efficient algorithm for finding the GCD of two natural numbers.

Here is a Python code that implements the Euclidean algorithm:

```
def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

# Example usage:
a = 10
b = 20
print(gcd(a, b))  # Output: 10
```

The Euclidean algorithm is named after the ancient Greek mathematician Euclid, who described it in his book "Elements" around 300 BC. The algorithm is based on the idea that the GCD of two numbers is the same as the GCD of the smaller number and the remainder of the larger number divided by the smaller number.

In the code, the function `gcd` takes two natural numbers `a` and `b` as input. It uses a `while` loop to repeatedly divide the larger number by the smaller number until the remainder is zero. The `a % b` operation calculates the remainder of `a` divided by `b`.

The code starts with `a` and `b` as the initial values. In each iteration of the loop, it swaps `a` and `b` so that `a` is always the smaller number. Then, it calculates the remainder of `a` divided by `b` and assigns it to `b`. When `b` becomes zero, the loop terminates, and `a` contains the GCD of the original `a` and `b`.

The code handles the case where `a` is smaller than `b` by swapping them before the loop. This ensures that `a` is always the smaller number in the loop.

The code also handles the case where `a` or `b` is zero. In this case, the GCD is the other number, so the code returns the non-zero number.

The Euclidean algorithm is a well-known and efficient algorithm for finding the GCD of two natural numbers. It is often used in computer science and mathematics.