How to write a minimum divisor problem?

Question

Python

Given an integer not less than 2. Print its least natural divisor different from 1.
When you first enter a number less than 2, and then more than two, it gives an error
. And when you immediately enter a number greater than two, everything is fine
b = 1
while True:
a = int (input())
b = b + 1
if a % b == 0:
print(b)
break
else:
if a < 2:
print("Error!")
continue

Answer 1

else:
if a < 2:
print("Ошибка!")
continue

Right here.
You need to check the value of the number before division. If less, then break .

Answer 2

def small_div(num):
    if num < 2:
        return f'Число не соответствует условию задачи: {num} < 2'
    for i in range(2, num+1):
        if not num%i:
            return i

Answer 3

There is a special Euclid algorithm for the largest divisor:
a = int(input())
b = int(input())
while a != 0 and b != 0:
if a > b:
a %= b
else :
b %= a
gcd = a+b
print(gcd)
you just need to change it a bit