Program to find the kth factor of n using Python

Suppose we have two positive values n and k. Now consider we have a list of all factors of n sorted in ascending order, we have to find the kth factor in this list. If there are less than k factors, then return -1.

So, if the input is like n = 28 k = 4, then the output will be 7 because, the factors of 28 are [1,2,4,7,14,28], fourth one is 7.

To solve this, we will follow these steps −

• if k is same as 1, then

  • return 1

• cand := a list with one element [1]

• for i in range 2 to 1 + floor of(square root of n), do

  • if n mod i is same as 0, then

    • insert i at the end of cand

  • m := size of cand

• if k > 2*m or (k is same as 2*m and n = (last element of cand)^2)

  • return -1

• if k <= m, then

  • return cand[k-1]

• factor := cand[2*m - k]

• return quotient of n/factor

Let us see the following implementation to get better understanding −

Example

from math import floor
def solve(n ,k):
   if k == 1:
      return 1
   cand = [1]
   for i in range(2, 1+floor(pow(n, 0.5))):
      if n%i == 0:
         cand.append(i)
      m = len(cand)
      if k > 2*m or (k == 2*m and n == cand[-1]**2):
         return -1
      if k <= m:
         return cand[k-1]
      factor = cand[2*m - k]
      return n//factor
n = 28
k = 4
print(solve(n ,k))

Input

28, 4

Output

7