Python中的gcd()

原文:https://www.geeksforgeeks.org/gcd-in-python/

最高公因数(HCF)，也称为 gcd，可以在 python 中使用数学模块提供的单个函数来计算，因此可以在许多情况下使任务变得更容易。

计算 gcd 的简单方法 *Using Recursion:

```py
# Python code to demonstrate naive
# method to compute gcd ( recursion )
def hcfnaive(a,b):
    if(b==0):
        return a
    else:
        return hcfnaive(b,a%b)
a = 60
b= 48
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (hcfnaive(60,48))
```
输出:
```py
The gcd of 60 and 48 is : 12
```** * ****Using [Loops](https://www.geeksforgeeks.org/loops-in-python/)
```py
# Python code to demonstrate naive
# method to compute gcd ( Loops )
def computeGCD(x, y):
    if x > y:
        small = y
    else:
        small = x
    for i in range(1, small+1):
        if((x % i == 0) and (y % i == 0)):
            gcd = i
    return gcd
a = 60
b= 48
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (computeGCD(60,48))
```
输出:
```py
The gcd of 60 and 48 is : 12
```**** * ******Using [Euclidean Algorithm](https://www.geeksforgeeks.org/basic-and-extended-euclidean-algorithms/)
```py
# Python code to demonstrate naive
# method to compute gcd ( Euclidean algo )
def computeGCD(x, y):
   while(y):
       x, y = y, x % y
   return x
a = 60
b= 48
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (computeGCD(60,48))
```
输出:
```py
The gcd of 60 and 48 is : 12
```
**使用 Python 的 math.gcd()函数**
使用 gcd()只需一行就可以计算出相同的 gcd。
```py
math.gcd( x, y )
Parameters :
x : Non-negative integer whose gcd has to be computed.
y : Non-negative integer whose gcd has to be computed.
Return Value :
This method will return 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.
```
```py
# Python code to demonstrate gcd()
# method to compute gcd
import math
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (math.gcd(60,48))
```
输出:
```py
The gcd of 60 and 48 is : 12
```
**常见异常**
此功能中的一些常见异常有:
* 两个数字都是 0，gcd 是 0
* 如果只有一个数字不是数字，则会引发类型错误。
```py
# Python code to demonstrate gcd()
# method exceptions
import math
# prints 0
print ("The gcd of 0 and 0 is : ",end="")
print (math.gcd(0,0))
# Produces error
print ("The gcd of a and 13 is : ",end="")
print (math.gcd('a',13))
```
输出:
```py
The gcd of 0 and 0 is : 0
The gcd of a and 13 is :
```
运行时错误:
```py
Traceback (most recent call last):
File "/home/94493cdfb3c8509146254862d12bcc97.py", line 12, in
print (math.gcd('a',13))
TypeError: 'str' object cannot be interpreted as an integer
```
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