In order to find the trailing zero in a given factorial, let us consider three examples as explained below −
Example 1
Input − 4
Output − 0
Explanation − 4! = 24, no trailing zero.
Factorial 4! = 4 x 3 x 2x 1 = 24. No trailing zero i.e. at 0’s place 4 number is there.
Example 2
Input − 6
Output − 1
Explanation − 6! = 720, one trailing zero.
Factorial 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720, one trailing zero, because at 0’s place 0 number is there.
Example 3
The input is as follows −
n = 4 n = 5
The output is as follows −
No − of trailing zeroes of 4! is 0
N0 − of trailing zeroes of 5! is 1
Example
Following is the C program to find the trailing zero in a given factorial −
#include <stdio.h>
static int trailing_Zeroes(int n){
int number = 0;
while (n > 0) {
number += n / 5;
n /= 5;
}
return number;
}
int main(void){
int n;
printf("enter integer1:");
scanf("%d",&n);
printf("\n no: of trailing zeroe's of factorial %d is %d\n\n ", n, trailing_Zeroes(n));
printf("enter integer2:");
scanf("%d",&n);
printf("\n no: of trailing zeroe's of factorial %d is %d ", n, trailing_Zeroes(n));
return 0;
}Output
When the above program is executed, it produces the following result −
enter integer1:5 no: of trailing zeroe's of factorial 5 is 1 enter integer2:6 no: of trailing zeroe's of factorial 6 is 1