Here is the Python code that implements the steps you provided:

```python
def euclidean_division(x, y):
    if x <= 0 or y <= 0:
        return "Input values must be positive integers."

    a = max(x, y)
    b = min(x, y)

    while b != 0:
        a, b = b, a % b

    return a

# Input values
num1 = 48
num2 = 18

result = euclidean_division(num1, num2)
print("Result:", result)
```

In this code:
- The `euclidean_division` function takes two positive integer inputs, finds the larger and smaller values, and performs the Euclidean division until the remainder is 0.
- If either of the input values is not a positive integer, the function returns a message stating that the values must be positive integers.
- The code then applies the function with example values 48 and 18 and prints the result.

You can change the values of `num1` and `num2` to test the function with different positive integers.