algorithm-in-python/math/numberTheory/gcd.py

#coding: utf-8
''' mbinary
#######################################################################
# File : gcd.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-12-16  10:06
# Description: 
#######################################################################
'''

def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a

def lcm(a,b):
    return int(a*b/gcd(a,b))
def xgcd(a,b):
    '''return gcd(a,b),  x,y  where  ax+by=gcd(a,b)'''
    if b==0:return a,1,0
    g,x,y = xgcd(b,a%b)
    return g,y,x-a//b*y

if __name__=='__main__':
    while 1:
        a = int(input('a: '))
        b = int(input('b: '))
        print('gcd :',gcd(a,b))
        print('xgcd:',xgcd(a,b))