The process you described is known as the Euclidean algorithm. It is an algorithm for finding the greatest common divisor of two integers. In your case, you are describing a way to find the denominator of the division that has a remainder of 0, which can be achieved by applying the Euclidean algorithm recursively.

Here is a Python implementation of the recursive function that replicates the process you described:

```python
def find_denominator(a, b):
    if b == 0:
        return a
    else:
        q = a // b
        r = a % b
        return find_denominator(b, r)

# Test the function
a = 357
b = 234
result = find_denominator(max(a,b), min(a,b))
print("Denominator of the division with remainder 0 =", result)
```

You can input any two natural numbers "a" and "b" to find the denominator of the division that has a remainder of 0 using this function.