# GCD of two number in python

You can use the built-in `math.gcd()` function to find the greatest common divisor of two numbers in Python. Here’s an example:

```import math

a = 48
b = 60

gcd = math.gcd(a, b)

print("The GCD of", a, "and", b, "is", gcd)
```

Output:

```The GCD of 48 and 60 is 12
```

In this example, we first import the `math` module, which provides the `gcd()` function. We then assign the values of the two numbers to `a` and `b`. Finally, we use the `math.gcd()` function to calculate the GCD of `a` and `b`, and print the result.

### GCD Using recursion:

You can also calculate the GCD of two numbers using recursion in Python. Here’s an example of a recursive function to find the GCD of two numbers:

```def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)

a = 48
b = 60

gcd_result = gcd(a, b)

print("The GCD of", a, "and", b, "is", gcd_result)
```

Output:

```The GCD of 48 and 60 is 12
```

In this example, the `gcd()` function takes two arguments `a` and `b`. It uses recursion to calculate the GCD of `a` and `b`. If `b` is equal to 0, then the function returns `a`, which is the GCD. Otherwise, it calls itself with `b` and `a % b` as arguments until `b` becomes 0.

Finally, we call the `gcd()` function with the values of `a` and `b`, and print the result.

### GCD Using the Loop:

You can also calculate the GCD of two numbers using a loop in Python. Here’s an example of a loop-based function to find the GCD of two numbers:

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

a = 48
b = 60

gcd_result = gcd(a, b)

print("The GCD of", a, "and", b, "is", gcd_result)
```

Output:

```The GCD of 48 and 60 is 12
```

In this example, the `gcd()` function takes two arguments `a` and `b`. It uses a loop to calculate the GCD of `a` and `b`. In each iteration of the loop, the function calculates the remainder of `a` divided by `b` using the modulo operator `%`, and stores it in a temporary variable `temp`. It then updates `a` to be equal to `b`, and `b` to be equal to `temp`. This process is repeated until `b` becomes 0.

Finally, the function returns `a`, which is the GCD of the two input numbers.

We then call the `gcd()` function with the values of `a` and `b`, and print the result.

### GCD Using Euclid’s algorithm or Euclidean Algorithm:

Euclid’s algorithm, also known as the Euclidean algorithm, is a commonly used algorithm to find the GCD of two numbers. Here’s an example of a function that implements Euclid’s algorithm in Python:

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

a = 48
b = 60

gcd_result = gcd(a, b)

print("The GCD of", a, "and", b, "is", gcd_result)
```

Output:

```The GCD of 48 and 60 is 12
```

In this example, the `gcd()` function takes two arguments `a` and `b`. It uses a loop to calculate the GCD of `a` and `b` using Euclid’s algorithm. In each iteration of the loop, the function updates `a` to be equal to `b`, and `b` to be equal to the remainder of `a` divided by `b` using the modulo operator `%`. This process is repeated until `b` becomes 0.

Finally, the function returns `a`, which is the GCD of the two input numbers.

We then call the `gcd()` function with the values of `a` and `b`, and print the result.