求两个数的gcd的Python程序

给定两个数字。任务是找到两个数字的 GCD。

使用 STL ：

在Python中， math 模块包含许多数学运算，可以使用该模块轻松执行。 math.gcd()函数计算其参数中提到的 2 个数字的最大公约数。

Syntax: math.gcd(x, y)

Parameter:

x : Non-negative integer whose gcd has to be computed.

y : Non-negative integer whose gcd has to be computed.

Returns: An absolute/positive integer value after calculating the GCD of given parameters x and y.

Exceptions: When Both x and y are 0, function returns 0, If any number is a character, Type error is raised.

Python3

# Python code to demonstrate the working of gcd()
# importing "math" for mathematical operations
import math
  
# prints 12
print("The gcd of 60 and 48 is : ", end="")
print(math.gcd(60, 48))

输出

The gcd of 60 and 48 is : 12

使用递归：

蟒蛇3

# Python code to demonstrate naive
# method to compute gcd ( recursion )
  
  
def hcf(a, b):
    if(b == 0):
        return a
    else:
        return hcf(b, a % b)
  
a = 60
b = 48
  
# prints 12
print("The gcd of 60 and 48 is : ", end="")
print(hcf(60, 48))

输出

The gcd of 60 and 48 is : 12

使用欧几里得算法：

欧几里得算法（或欧几里得算法）是一种有效地找到两个数的最大公约数 (GCD) 的方法。两个整数 X 和 Y 的 GCD 是将 X 和 Y 整除的最大数（不留余数）。

算法伪代码-

1. 设 a, b 为两个数
2. 模 b = R
3. 设 a = b 且 b = R
4. 重复步骤 2 和 3，直到 a mod b 大于 0
5. GCD = b
6. 结束

蟒蛇3

# Recursive function to return gcd of a and b
def gcd(a, b):
  
    # Everything divides 0
    if (a == 0):
        return b
    if (b == 0):
        return a
  
    # base case
    if (a == b):
        return a
  
    # a is greater
    if (a > b):
        return gcd(a-b, b)
    return gcd(a, b-a)
  
# Driver program to test above function
a = 98
b = 56
if(gcd(a, b)):
    print('GCD of', a, 'and', b, 'is', gcd(a, b))
else:
    print('not found')

输出

GCD of 98 and 56 is 14