# How to Find GCD or HCF in Python using gcd() Function

GCD stands for greatest common divisor. It is sometimes called highest common factor or divisor (HCF or HCD). We can define GCD or HCF as:

“GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of any two given numbers `x` and `y` is the largest positive number that divides both `x` and `y` numbers with zero remainders, where at least one of the numbers `x` and `y` is nonzero”.

For instance, the GCD of number 6 and 9 is 3.
For example:
The divisors of 6 are 1,2,3,6 and the divisors of 9 are 1,2,3,9.
If you notice carefully, 3 is the greatest factor that divides both 6 and 9 with zero remainders hence 3 is GCD or HCF of 6 and 9.

## `gcd()` Function in Python

Python Standard math Library provides a built-in function `gcd()` to calculate GCD or HCF of any two or more given numbers.

## Syntax of `gcd()` Function

The syntax of `gcd()` function in Python is:
`math.gcd( x, y )`

## Parameters of `gcd()` function

`x` Any valid Python integer. This parameter is required.
`y` Any valid Python integer. This parameter is required.
Note: `math.gcd()` function uses at least two parameters to calculate GCD. That is why both parameters are required.

Python 2.x – Yes
Python 3.x – Yes

## Return Value of `gcd()` in Python

Python `gcd()` function will return an absolute/positive integer value after calculating the GCD of given parameters `x` and `y`.

## Common programming errors in `gcd()` function

If either `x` or `y` argument is zero, `gcd()` function returns `TypeError`
If data type of `x` or `y` argument is not a number, `gcd()` function returns `TypeError`.

## Points to Ponder

If both `x` and `y` values are zero, `gcd()` returns `zero`
If none of the parameters is zero `gcd()` function returns a nonzero value.

## Python `gcd()` Function Example

Output of Python `gcd()` function:
`6 100 6 2 0`