Problem: Given are positive integers A and B.  Let us choose some number of positive common divisors of A and B.  Here, any two of the chosen divisors must be coprime.  At most, how many divisors can we choose?  Definition of common divisor  An integer d is said to be a common divisor of integers x and y when d divides both x and y.  Definition of being coprime  Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.  Definition of dividing  An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Submission attempts (in order):
import math

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr
  
d = gcd(a,b)


from fractions import gcd

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr
  
d = gcd(a,b)


import math

a,b=map(int,input().split())

def factorization(n):
  factor=[]
  tmp=int(math.sqrt(n))+1
  for num in range(2,tmp):
    while n%num==0:
      n//=num
      factor.append(num)
      break
    if not factor:
      return 'prime number'
    else:
      factor.append(n)
      return factor
a_list=factorization(a)
b_list=factorization(b)

a_b_and=set(a_list)&set(b_list)
print(len(a_b_and)+1)

import math

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr
  
a_list = factorization(a)
b_list = factorization(b)

a_b_and = set(a_list) & set(b_list)
print(len(a_b_and) + 1)


from fractions import gcd

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr
  
d = gcd(a,b)
print(len(factorization(d)) + 1) 

import math

a,b=map(int,input().split())

def factorization(n):
  factor=[]
  tmp=int(math.sqrt(n))+1
  for num in range(2,tmp):
    while n%num==0:
      n//=num
      factor.append(num)
      break
    if not factor:
      return 'prime number'
    else:
      factor.append(n)
      return factor

a_list=factorization(a)
b_list=factorization(b)

a_b_and=set(a_list)&set(b_list)
print(len(a_b_and)+1)


import math

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr
  
d = math.gcd(a,b)


import math

a,b=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(math.sqrt(n))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)
    return arr
  
a_list = factorization(a)
b_list = factorization(b)

a_b_and = set(a_list) & set(b_list)
print(len(a_b_and) + 1)


Verdicts: Runtime Error

Wrong Answer

Runtime Error

Runtime Error

Wrong Answer

Runtime Error

Runtime Error

Accepted