# Print the kth common factor of two numbers

Given with two numbers x and y the output should contain their kth common factor.

Input: x=9 y=18 k=1
Output : k common factor = 2
Factors of 9 : 1, 3, 9
Factors of 18 : 1, 2, 3, 6, 9, 18
Greatest Common Factor : 9

## Algorithm

START
Step 1 -: take input as x and y lets say 3 and 21 and k as 1
Step 2 -: declare start variables as int i,num,count=1
Step 3 -: IF x<y
Set num=x
End IF
Step 4 -: Else
Set num=y
End Else
Step 5 -: Loop For i=2and i<=num and i++
IF x % i==0 and y % i == 0
Count =count +1
End If
IF count=k
Print i
End IF
Else
Return -1
End Else
Step 6 -: End Loop For
STOP

## Example

#include<stdio.h>
int main() {
int x = 3, y = 21, k = 1; // taking x and y as two number and k is limit for their common factor
int i,num,count=1;
if(x<y) //fetching smaller value in num[poi
num=x;
else
num=y;
for (i=2; i<=num; i++) { //loop from 2 till smaller value
if (x % i==0 && y % i == 0) //if remainder is 0 increment count
count++;
if (count == k)
printf("%d",i);
else
printf("no value as there are less factors than k between x and y ");
break;
}
return 0;
}

## Output

if we run above program then it will generate following output.

their kth common factor is : 2