Python Program for GCD of more than two (or array) numbers

The GCD of three or more numbers equals the product of the prime factors common to all the numbers, but it can also be calculated by repeatedly taking the GCDs of pairs of numbers.

gcd(a, b, c) = gcd(a, gcd(b, c)) 
             = gcd(gcd(a, b), c) 
             = gcd(gcd(a, c), b)

Python

# GCD of more than two (or array) numbers
# This function implements the Euclidean
# algorithm to find H.C.F. of two number

def find_gcd(x, y):
    while(y):
        x, y = y, x % y

    return x


l = [2, 4, 6, 8, 16]

num1=l[0]
num2=l[1]
gcd=find_gcd(num1,num2)

for i in range(2,len(l)):
    gcd=find_gcd(gcd,l[i])

print(gcd)

# Code contributed by Mohit Gupta_OMG

Output:

2

Time complexity :  O(n + log(min(a, b))), as the function goes through the list of numbers and finds the GCD for each pair of numbers using the Euclidean algorithm.
Auxiliary Space: O(log x), as the function only uses a few variables to store the GCD and the numbers being compared.

Please refer complete article on GCD of more than two (or array) numbers for more details!