Find Highest Common Factor of a List of Elements in Python

Suppose we have a list of elements called nums, we have to find the largest positive value that divides each of the integers.

So, if the input is like nums = [15, 81, 78], then the output will be 3, as 3 is the largest integer that divides all 15, 81, and 78.

To solve this, we will follow these steps −

• if size of nums is same as 1, then

  • return nums[0]

• div := gcd of nums[0] and nums[1])

• if size of nums is same as 2, then

  • return div

• for i in range 1 to size of nums - 2, do

  • div := gcd of div and nums[i + 1]

  • if div is same as 1, then

    • return div

• return div

Example

Let us see the following implementation to get better understanding

from math import gcd
def solve(nums):
   if len(nums) == 1:
      return nums[0]

   div = gcd(nums[0], nums[1])

   if len(nums) == 2:
      return div

   for i in range(1, len(nums) - 1):
      div = gcd(div, nums[i + 1])
      if div == 1:
         return div

return div

nums = [15, 81, 78]
print(solve(nums))

Input

[15, 81, 78]

Output

3