Python function that returns true if 2 integers are coprime

Question

I need some help to find my bugs in this function:

def is_coprime(num_1, num_2):
    """Function that returns true if 2 integers are coprime. """
    if num_1 > num_2:
        small = num_2
    else:
        small = num_1
    for i in range(1, small + 1):
        if ((num_1 % i == 0) and (num_2 % i != 0)):
            gcd = i
        if (gcd == 1):
            return True
        else:
            return False

Hope the indentation isn't so bad. I think my mistake is in the if-condition, but I can't figure out what.

Answer 1

I would suggest this approach:

def divisors(x):
    return {i for i in range(2, x//2 + 1) if not x % i}

def coprime(x, y):
    return divisors(x).isdisjoint(divisors(y))

How does it work? divisors(x) returns the set f all divisors of a number greater than 1. The coprie(x, y) function check, if given sets are disjoint.