Buggy python submission (verdict: Time Limit Exceeded):
# 初期入力
A,B = (int(x) for x in input().split())

#公約数を求める
def kouyakusu(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf

#約数 #商と割る数をタプルで返す
def yakusu_tapulu(n):# 商と割る数 両方を返す
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            syou,amari =divmod(n,i)
            divisors.append((syou,i))
    return divisors

#公約数の約数をタプルで作る。互いに素だから要素数は「１」
x_yakusu =[]
x_kouyaku = kouyakusu(A,B) #A,Bの公約数＿リスト
count =0
for i in x_kouyaku:
    a_yakusu = yakusu_tapulu(i)
    if len(a_yakusu) ==1:
        count +=1
        #x_yakusu.append(yakusu_tapulu(i))
print(count)

Fixed submission:
# 初期入力
A,B = (int(x) for x in input().split())

#素因数分解
def soinsu_bunkai(m):
    pf={}

    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:
        pf[m]=1
    return pf
# 入力値A,Bを素因数分解
A_soinsu =soinsu_bunkai(A)
B_soinsu =soinsu_bunkai(B)

#共通の素数を探す
kyotu_soinsu ={}
a_sosu ={i for i in A_soinsu.keys()}
b_sosu ={i for i in B_soinsu.keys()}
kotae = a_sosu & b_sosu

print(len(kotae)+1) # 素数「１」を足す

Buggy python submission (verdict: Time Limit Exceeded):
# 初期入力
A,B = (int(x) for x in input().split())

#公約数を求める
def kouyakusu(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf

#約数 #商と割る数をタプルで返す
def yakusu_tapulu(n):# 商と割る数 両方を返す
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            syou,amari =divmod(n,i)
            divisors.append((syou,i))
    return divisors

#公約数の約数をタプルで作る。互いに素だから要素数は「１」
x_yakusu =[]
x_kouyaku = kouyakusu(A,B) #公約数のリスト
x_yakusu =[yakusu_tapulu(i) for i in x_kouyaku  if len(yakusu_tapulu(i)) ==1]
print(len(x_yakusu))

Fixed submission:
# 初期入力
A,B = (int(x) for x in input().split())

#素因数分解
def soinsu_bunkai(m):
    pf={}

    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:
        pf[m]=1
    return pf
# 入力値A,Bを素因数分解
A_soinsu =soinsu_bunkai(A)
B_soinsu =soinsu_bunkai(B)

#共通の素数を探す
kyotu_soinsu ={}
a_sosu ={i for i in A_soinsu.keys()}
b_sosu ={i for i in B_soinsu.keys()}
kotae = a_sosu & b_sosu

print(len(kotae)+1) # 素数「１」を足す

Buggy python submission (verdict: Runtime Error):
#公約数を求める
def kouyakusu(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf

#約数 #商と割る数をタプルで返す
def yakusu_tapulu(n):# 商と割る数 両方を返す
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            syou,amari =divmod(n,i)
            divisors.append((syou,i))
    return divisors

#公約数の約数をタプルで作る。互いに素だから要素数は「１」
x_yakusu =[]
x_kouyaku = kouyakusu(A,B) #公約数のリスト
x_yakusu =[yakusu_tapulu(i) for i in x_kouyaku  if len(yakusu_tapulu(i)) ==1]
print(len(x_yakusu))

Fixed submission:
# 初期入力
A,B = (int(x) for x in input().split())

#素因数分解
def soinsu_bunkai(m):
    pf={}

    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:
        pf[m]=1
    return pf
# 入力値A,Bを素因数分解
A_soinsu =soinsu_bunkai(A)
B_soinsu =soinsu_bunkai(B)

#共通の素数を探す
kyotu_soinsu ={}
a_sosu ={i for i in A_soinsu.keys()}
b_sosu ={i for i in B_soinsu.keys()}
kotae = a_sosu & b_sosu

print(len(kotae)+1) # 素数「１」を足す