Buggy python submission (verdict: Time Limit Exceeded):
import math as m
import fractions

A, B = list(map(int, input().split()))
#A , B = 12, 18

def sieve_of_eratosthenes(n):
    candidate = [1 for i in range(n+1)]
    candidate[0] = 0
    candidate[1] = 0
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(m.floor(A**0.5))
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

#pf = prime_factorize(fractions.gcd(A, B))
# num = 1

# for x in pf:
#     if x >= 1:
#         num = num + 1



# print(num)

g = fractions.gcd(A,B)
primes = []
num = 1

if True:
    i = 2
    if (g % i == 0):
        cnt = 0
        while g % i == 0:
            cnt = cnt + 1
            g = g // i
        primes.append([i, cnt])
    i = i + 1
    while i <= g:
        if (g % i == 0):
            cnt = 0
            while g % i == 0:
                cnt = cnt + 1
                g = g // i
            primes.append([i, cnt])
        i = i + 2

print(len(primes)+1)


Fixed submission:
import math as m
import fractions

A, B = list(map(int, input().split()))
#A , B = 12, 18

def sieve_of_eratosthenes(n):
    candidate = [1 for i in range(n+1)]
    candidate[0] = 0
    candidate[1] = 0
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(m.floor(A**0.5))
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

#pf = prime_factorize(fractions.gcd(A, B))
# num = 1

# for x in pf:
#     if x >= 1:
#         num = num + 1



# print(num)

g = fractions.gcd(A,B)
primes = []
num = 1

if True:
    i = 2
    while i * i <= g:
        if (g % i == 0):
            cnt = 0
            while g % i == 0:
                cnt = cnt + 1
                g = g // i
            primes.append([i, cnt])
        i = i + 1
    if (g != 1):
        primes.append([g, 1])
print(len(primes)+1)

Buggy python submission (verdict: Time Limit Exceeded):
import math as m
import fractions

A, B = list(map(int, input().split()))
#A , B = 12, 18

def sieve_of_eratosthenes(n):
    candidate = [1 for i in range(n+1)]
    candidate[0] = 0
    candidate[1] = 0
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(m.floor(A**0.5))
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

#pf = prime_factorize(fractions.gcd(A, B))
# num = 1

# for x in pf:
#     if x >= 1:
#         num = num + 1



# print(num)

g = fractions.gcd(A,B)
primes = []
num = 1

if True:
    i = 2
    while i <= g:
        if (g % i == 0):
            cnt = 0
            while g % i == 0:
                cnt = cnt + 1
                g = g // i
            primes.append([i, cnt])
        i = i + 1


#print(primes)
print(len(primes)+1)


Fixed submission:
import math as m
import fractions

A, B = list(map(int, input().split()))
#A , B = 12, 18

def sieve_of_eratosthenes(n):
    candidate = [1 for i in range(n+1)]
    candidate[0] = 0
    candidate[1] = 0
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(m.floor(A**0.5))
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

#pf = prime_factorize(fractions.gcd(A, B))
# num = 1

# for x in pf:
#     if x >= 1:
#         num = num + 1



# print(num)

g = fractions.gcd(A,B)
primes = []
num = 1

if True:
    i = 2
    while i * i <= g:
        if (g % i == 0):
            cnt = 0
            while g % i == 0:
                cnt = cnt + 1
                g = g // i
            primes.append([i, cnt])
        i = i + 1
    if (g != 1):
        primes.append([g, 1])
print(len(primes)+1)

Buggy python submission (verdict: Runtime Error):
import math as m

A, B = list(map(int, input().split()))
#A , B = 12, 18
def lcm(a, b):
    return (A * B) // m.gcd(A, B)

def sieve_of_eratosthenes(n): # n以下の素因数を求める
    candidate = [1 for i in range(n+1)]
    candidate[0:2] = [0 , 0]
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(A)
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

pf = prime_factorize(m.gcd(A, B))
num = 1

for x in pf:
    if x >= 1:
        num = num + 1

print(num)


Fixed submission:
import math as m
import fractions

A, B = list(map(int, input().split()))
#A , B = 12, 18

def sieve_of_eratosthenes(n):
    candidate = [1 for i in range(n+1)]
    candidate[0] = 0
    candidate[1] = 0
    for i in range(len(candidate)):
        if (candidate[i] == 0):
            continue
        j = 2
        while j * i < len(candidate):
            candidate[i * j] = 0
            j = j + 1
    primes = [i for i in range(n) if candidate[i] == 1]
    return primes

def prime_factorize(A):
    p = sieve_of_eratosthenes(m.floor(A**0.5))
    a = [0 for i in p]
    for i in range(len(p)):
        if A % p[i] != 0:
            a[i] = 0
        else:
            temp = A
            while temp % p[i] == 0:
                temp = temp / p[i]
                a[i] = a[i] + 1
    return a

#pf = prime_factorize(fractions.gcd(A, B))
# num = 1

# for x in pf:
#     if x >= 1:
#         num = num + 1



# print(num)

g = fractions.gcd(A,B)
primes = []
num = 1

if True:
    i = 2
    while i * i <= g:
        if (g % i == 0):
            cnt = 0
            while g % i == 0:
                cnt = cnt + 1
                g = g // i
            primes.append([i, cnt])
        i = i + 1
    if (g != 1):
        primes.append([g, 1])
print(len(primes)+1)