N-GCD

    if num==2:
        return True
    length = max(int(pow(num,0.5))+1,3)
    for i in range(2,length):
        if num%i==0:
            return False
    return True  
def dp(dui):
    def find_yue(dui,yue):
        if yue==[]:
            return -1
        if dui==[]:
            return yue
        new_yue = []
        for i in yue:
            if dui[0][0]%i==0 or dui[0][1]%i==0:
                new_yue.append(i)
        dui.remove(dui[0])
        return find_yue(dui,new_yue)


    yue = [i+1 for i in range(1,max(dui[0]))]
    out = find_yue(dui,yue)
    if out==-1:
        print(-1)
    else:
        lth = len(out)
        for i in range(lth):
            if fig(out[lth-i-1]):
                print(out[lth-i-1])
                break
def prtable(dui,mi):
    tab = []
    for i in range(2,mi+1):
        if fig(i):
            tab.append(i)
    for i in range(len(dui)):
        for j in tab:
            if dui[i][0]%j and dui[i][1]%j:
                tab.remove(j)
    if tab==[]:
        print(-1)
    else:
        print(tab[-1])
                
    return 0
if __name__=='__main__':
    n = int(input())
    dui = []
    mi=2*10e9
    for i in range(n):
        _dui = list(map(lambda x:int(x),input().split(' ')))
        mi = min(mi,min(_dui))
        dui.append(_dui)
    
    #dp(dui)
    prtable(dui,mi)

分析

在读取数字的时候顺便计算下最小值min，之后找出[2,min]之间的素数，并从大到小遍历，判断该数能否整除除nums数组中每一个数对中的任意一个值。

from math import sqrt

def is_prime(a):
    for i in range(2,int(sqrt(a)+1)):
        if a%i==0:
            return False
    return True

N = int(input())
nums = []
min_val = 1e9
for i in range(N):
    val1,val2 = list(map(int,input().split()))
    min_val = min(min_val,val1,val2)
    nums.append([val1,val2])

primes = []
res = 1e9
for i in range(min_val,1,-1):
    if is_prime(i):
        primes.append(i)

for val in primes:
    satisfied = True
    for i in range(N):
        if nums[i][0]%val!=0 and nums[i][1]%val!=0:
            satisfied = False
            break
    if satisfied:
        res = val
        break

print(res) if res!=1e9 else print(-1)