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

import math
def Sieve_of_Eratosthenes(N):
    if N<2: return set()
    prime=set(i for i in range(2,N+1))
    for i in range(2,math.ceil(N**0.5)+1):
        tmp=set()
        for j in prime:
            if j>i and j%i==0: tmp.add(j)
        for j in tmp:
            prime.remove(j)

    return prime

def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
n=gcd(a,b)
prime=list(Sieve_of_Eratosthenes(int(math.sqrt(n))+2))

ans=1
x=n
for p in prime:
    if x==1:
        break
    if x%p==0:
        ans+=1
        while x%p==0:
            x=x//p

if x!=1: ans+=1
print(ans)


Fixed submission:
import math
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
x=gcd(a,b)
s=set()
for i in range(2, min(x+1,int(math.sqrt(x))+2) ):
    while x%i==0:
        x=x//i
        s.add(i)
    if x==1: break
if x>1: s.add(x)
print(len(s)+1)

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

import math
def Sieve_of_Eratosthenes(N):
    if N<2: return set()
    prime=set(i for i in range(2,N+1))
    for i in range(2,math.ceil(N**0.5)+1):
        tmp=set()
        for j in prime:
            if j>i and j%i==0: tmp.add(j)
        for j in tmp:
            prime.remove(j)

    return prime

def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
n=gcd(a,b)
prime=Sieve_of_Eratosthenes(int(math.sqrt(n))+2)

dic={}
ans=1
x=n
for p in prime:
    if x==1:
        break
    if x%p==0:
        ans+=1
        while x%p==0:
            x=x//p

if x!=1: ans+=1
print(ans)

Fixed submission:
import math
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
x=gcd(a,b)
s=set()
for i in range(2, min(x+1,int(math.sqrt(x))+2) ):
    while x%i==0:
        x=x//i
        s.add(i)
    if x==1: break
if x>1: s.add(x)
print(len(s)+1)

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

import math
def Sieve_of_Eratosthenes(N):
    if N<2: return set()
    prime=set(i for i in range(2,N+1))
    for i in range(2,math.ceil(N**0.5)+1):
        tmp=set()
        for j in prime:
            if j>i and j%i==0: tmp.add(j)
        for j in tmp:
            prime.remove(j)

    return prime

def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
n=gcd(a,b)
prime=Sieve_of_Eratosthenes(int(math.sqrt(n))+2)

dic={}
ans=1
x=n
for p in prime:
    if x%p==0:
        ans+=1
        while x%p==0:
            x=x//p

if x!=1: ans+=1
print(ans)

Fixed submission:
import math
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
x=gcd(a,b)
s=set()
for i in range(2, min(x+1,int(math.sqrt(x))+2) ):
    while x%i==0:
        x=x//i
        s.add(i)
    if x==1: break
if x>1: s.add(x)
print(len(s)+1)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
x=gcd(a,b)
s=set()
while x>1:
    for i in range(2, min(x+1,int(math.sqrt(x))+2) ):
        while x%i==0:
            x=x//i
            s.add(i)
print(len(s)+1)

Fixed submission:
import math
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

a,b=map(int,input().split())
x=gcd(a,b)
s=set()
for i in range(2, min(x+1,int(math.sqrt(x))+2) ):
    while x%i==0:
        x=x//i
        s.add(i)
    if x==1: break
if x>1: s.add(x)
print(len(s)+1)