101201: [AtCoder]ABC120 B - K-th Common Divisor
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $200$ points
Problem Statement
You are given positive integers $A$ and $B$.
Find the $K$-th largest positive integer that divides both $A$ and $B$.
The input guarantees that there exists such a number.
Constraints
- All values in input are integers.
- $1 \leq A, B \leq 100$
- The $K$-th largest positive integer that divides both $A$ and $B$ exists.
- $K \geq 1$
Input
Input is given from Standard Input in the following format:
$A$ $B$ $K$
Output
Print the $K$-th largest positive integer that divides both $A$ and $B$.
Sample Input 1
8 12 2
Sample Output 1
2
Three positive integers divides both $8$ and $12$: $1, 2$ and $4$. Among them, the second largest is $2$.
Sample Input 2
100 50 4
Sample Output 2
5
Sample Input 3
1 1 1
Sample Output 3
1