The Kth Factor Of N · Interview Problem

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Leetcode

Medium

Math

Number Theory

Greedy

The Kth Factor Of N

Find the k-th positive divisor of an integer n in increasing order, or report that it does not exist.

Acceptance 0%

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Problem Statement

Given two integers $n$ and $k$ , consider all positive factors (divisors) of $n$ arranged in strictly increasing order. Return the factor that appears at position $k$ in this ordering.

If $n$ has fewer than $k$ positive factors, return $-1$ .

Your goal is to determine the answer efficiently without explicitly relying on a large, repeated search over all numbers up to $n$ .

Input Format

The input consists of two integers $n$ and $k$ .
$n$ is the number whose positive factors are being queried.
$k$ is the 1-indexed position of the factor to return.

Output Format

Return a single integer: the $k$ -th positive factor of $n$ in increasing order.
If fewer than $k$ factors exist, return $-1$ .

Constraints

$1 \le n$ and $1 \le k$ .
The answer is 1-indexed.
Factors are positive integers that divide $n$ evenly.

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 12, k = 3

Output

Explanation

The positive factors of 12 in increasing order are [1, 2, 3, 4, 6, 12]. The 3rd factor is 3.

Example 2

Input

n = 7, k = 2

Output

Explanation

The positive factors of 7 are [1, 7]. The 2nd factor is 7.

Show 1 more example

Example 3

Input

n = 4, k = 4

Output

-1

Explanation

The positive factors of 4 are [1, 2, 4], so there is no 4th factor.

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