1492. The kth Factor of n

Description

You are given two positive integers n and k. A factor of an integer n is defined as an integer i where n % i == 0.

Consider a list of all factors of n sorted in ascending order, return the kth factor in this list or return -1 if n has less than k factors.

 

Example 1:

Input: n = 12, k = 3
Output: 3
Explanation: Factors list is [1, 2, 3, 4, 6, 12], the 3rd factor is 3.

Example 2:

Input: n = 7, k = 2
Output: 7
Explanation: Factors list is [1, 7], the 2nd factor is 7.

Example 3:

Input: n = 4, k = 4
Output: -1
Explanation: Factors list is [1, 2, 4], there is only 3 factors. We should return -1.

 

Constraints:

• 1 <= k <= n <= 1000

 

Follow up:

Could you solve this problem in less than O(n) complexity?

 

Solutions

Solution: Math

• Time complexity: O(sqrt(n))
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @param {number} k
 * @return {number}
 */
const kthFactor = function (n, k) {
  const factors = [];

  for (let num = 1; num ** 2 <= n; num++) {
    if (n % num) continue;
    const factor = n / num;

    if (factor !== num) factors.push(factor);
    k -= 1;
    if (k === 0) return num;
  }
  return k > factors.length ? -1 : factors.at(-k);
};