My attempt to Euclid's Algorithm in Python

euclid's_algorithm.py

import math

num1 = int(input("First Number: "))
num2 = int(input("Second Number: "))


if (num1 > num2):
    while (math.fmod(num1, num2) != 0):
        if (num1 > num2):
            difference = num1 - num2
            num1 = num2
            if (num1 > difference):
                num2 = difference
            else:
                num1 = difference
            print(f"First Number: {num1} \nSecond Number: {num2}")
        else:
            difference = num2 - num1
            num2 = num1
            if (num2 > difference):
                num1 = difference
            print(f"First Number: {num1} \nSecond Number: {num2}")
    print(num2)
else:
    while (math.fmod(num2, num1) != 0):
        if (num2 > num1):
            difference = num2 - num1
            num1 = num2
            if (num2 > difference):
                num1 = difference
            else:
                num2 = difference
            print(f"First Number: {num2} \nSecond Number: {num1}")
        else:
            difference = num1 - num2
            num1 = num2
            if (num1 > difference):
                num2 = difference
            print(f"First Number: {num2} \nSecond Number: {num1}")
    print(num1)


print(f"First Number: {num1} \nSecond Number: {num2}")

There are more effective ways to write this