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())
C = min(A,B)
D = math.floor(math.sqrt(A))
E = math.floor(math.sqrt(B))
Num1 = set()
Num2 = set()
for i in range(1,D+1):
    if A%i == 0:
        Num1.add(i)
Num1.add(A)
for i in range(1,E+1):
    if B%i == 0:
        Num2.add(i)
Num2.add(B)
Num = Num2&Num1
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        raise ValueError('n is more than 2')
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
data = set(get_sieve_of_eratosthenes(10**6))
data.add(1)
Answer =Num&data
print(len(Answer))

import math
A,B = map(int,input().split())
C = min(A,B)
D = math.floor(math.sqrt(C))
Num1 = set()
Num2 = set()
for i in range(1,D+1):
    if A%i == 0:
        Num1.add(i)
for i in range(1,D+1):
    if B%i == 0:
        Num2.add(i)
Num = Num2&Num1
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        raise ValueError('n is more than 2')
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
data = set(get_sieve_of_eratosthenes(10**6))
Answer =Num&data
print(len(Answer))

import math
A,B = map(int,input().split())
C = min(A,B)
D = math.floor(math.sqrt(A))
E = math.floor(math.sqrt(B))
Num1 = set()
Num2 = set()
for i in range(1,10**6+1):
    if A%i == 0:
        Num1.add(i)
Num1.add(A)
for i in range(1,10**6+1):
    if B%i == 0:
        Num2.add(i)
Num2.add(B)
Num = Num2&Num1
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        raise ValueError('n is more than 2')
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
data = set(get_sieve_of_eratosthenes(10**6))
data.add(1)
Answer =Num&data
print(len(Answer))

import math
A,B = map(int,input().split())
C = min(A,B)
D = math.floor(math.sqrt(C))
Num1 = set()
Num2 = set()
for i in range(1,D+1):
    if A%i == 0:
        Num1.add(i)
for i in range(1,D+1):
    if B%i == 0:
        Num2.add(i)
Num = Num2&Num1
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        raise ValueError('n is more than 2')
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
data = set(get_sieve_of_eratosthenes(10**6))
data.add(1)
Answer =Num&data
print(len(Answer))

import math
A,B = map(int,input().split())
C = min(A,B)
D = math.floor(math.sqrt(C))
Num1 = set()
Num2 = set()
for i in range(1,D+1):
    if A%i == 0:
        Num1.add(i)
Num1.add(A)
for i in range(1,D+1):
    if B%i == 0:
        Num2.add(i)
Num2.add(2)
Num = Num2&Num1
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        raise ValueError('n is more than 2')
    prime = []
    limit = math.sqrt(n)
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if limit <= p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
data = set(get_sieve_of_eratosthenes(10**6))
data.add(1)
Answer =Num&data
print(len(Answer))

import math
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,B = map(int,input().split())
Af = factorization(A)
Bf = factorization(B)
As = set()
Bs = set()
for i in range(len(Af)):
    As.add(Af[i][0])
for j in range(len(Bf)):
    Bs.add(Bf[j][0])
if A == 1 and B ==1:
    print(1)
else:
    print(len(As & Bs)+1)

Verdicts: Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Accepted