gcd() in Python

gcd() function in Python is used to compute the Greatest Common Divisor (GCD) of two integers. It is available in the math module and returns the largest positive integer that divides both numbers without leaving a remainder. Example:

import math
a = 60
b = 48

print(math.gcd(a, b))

12

Explanation: The common divisors of 60 and 48 are [1, 2, 3, 4, 6, 12] and the greatest one is 12.

Syntax of math.gcd()

import math

math.gcd(x, y)

Parameters: x, y is Two non-negative integers (at least one of them must be non-zero).

Returns:

• The greatest common divisor of x and y.
• If either x or y is 0, the result is the absolute value of the non-zero number.

Examples of using math.gcd() function

Example 1: GCD of a number and 0

import math

print(math.gcd(0, 25))

25

Explanation: When one number is 0, the gcd() returns the absolute value of the other number.

Example 2: GCD of two co-prime numbers

import math

print(math.gcd(17, 29))

1

Explanation: 17 and 29 are co-prime (no common divisors except 1), so gcd() returns 1.

Example 3: GCD in a list of numbers using functools.reduce()

import math
from functools import reduce

nums = [48, 64, 80]

# Find GCD of the list
res = reduce(math.gcd, nums)
print(res)

16

Explanation: This finds the GCD of multiple numbers by applying math.gcd() cumulatively to the list elements.