Buggy python submission (verdict: Time Limit Exceeded):
from pprint import pprint
from fractions import gcd
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return divisors
a, b = map(int, input().split())
cd = sorted(list(make_divisors(a) & make_divisors(b)))
n = len(cd)
divs = [[False for _ in range(n)] for _ in range(n)]
choice = []
answer = 0
for i in cd:
    n = len(choice)
    for j in range(n):
        for k in choice[j]:
            if gcd(i, k) != 1:
                break
        else:
            addition = choice[j] + [i]
            if len(addition) > answer:
                answer = len(addition)
            choice.append(addition)
    choice.append([i])
print(answer if answer > 0 else 1)

Fixed submission:
from fractions import gcd
from math import sqrt
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return list(divisors)
def is_prime(n):
    if n == 1:
        return False
    for k in range(2, int(sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
a, b = map(int, input().split())
print(len([div for div in make_divisors(gcd(a, b)) if is_prime(div)]) + 1)

Buggy python submission (verdict: Time Limit Exceeded):
from pprint import pprint
from fractions import gcd
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return divisors
a, b = map(int, input().split())
cd = sorted(list(make_divisors(a) & make_divisors(b)))
n = len(cd)
divs = [[False for _ in range(n)] for _ in range(n)]
choice = []
answer = 0
for i in cd:
    n = len(choice)
    for j in range(n):
        for k in choice[j]:
            if gcd(i, k) != 1:
                break
        else:
            addition = choice[j] + [i]
            if len(addition) > answer:
                answer = len(addition)
            choice.append(addition)
    choice.append([i])
print(answer if answer != 0 else 1)

Fixed submission:
from fractions import gcd
from math import sqrt
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return list(divisors)
def is_prime(n):
    if n == 1:
        return False
    for k in range(2, int(sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
a, b = map(int, input().split())
print(len([div for div in make_divisors(gcd(a, b)) if is_prime(div)]) + 1)

Buggy python submission (verdict: Time Limit Exceeded):
from pprint import pprint
from fractions import gcd
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return divisors
a, b = map(int, input().split())
cd = sorted(list(make_divisors(a) & make_divisors(b)))
n = len(cd)
divs = [[False for _ in range(n)] for _ in range(n)]
choice = []
answer = 0
for i in cd:
    n = len(choice)
    for j in range(n):
        for k in choice[j]:
            if gcd(i, k) != 1:
                break
        else:
            addition = choice[j] + [i]
            if len(addition) > answer:
                answer = len(addition)
            choice.append(addition)
    choice.append([i])
print(answer if answer > 0 else 1)

Fixed submission:
from fractions import gcd
from math import sqrt
import sys
def input() -> str:
    return sys.stdin.readline()
def make_divisors(n):
    divisors = set()
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.add(i)
            divisors.add(n//i)
    return list(divisors)
def is_prime(n):
    if n == 1:
        return False
    for k in range(2, int(sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
a, b = map(int, input().split())
print(len([div for div in make_divisors(gcd(a, b)) if is_prime(div)]) + 1)