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Count trailing zeros in factorial of a number in C++
Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for that number. A factorial of a number N is a product of all numbers in the range [1, N].
We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of any number greater than 5, we have a number of 2s more than 5s in prime factorization of that number. Dividing a number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes.
For Example
Input
number=6
Output
Count of trailing zeros in factorial of a number are: 1
Explanation
The factorial is 30. Prime factors of 30 : 2 * 3 * 5 So only one pair of (2,5) exists so trailing zeros is 1.
Input
number=12
Output
Count of trailing zeros in factorial of a number are: 2
Explanation
The factorial is 479001600. Prime factors of 479001600 : 210 x 35 x 52 x 71 x 111 So we can get 2 pairs of (2,5) so trailing zeros are 2
Approach used in the below program is as follows −
In this approach we will divide the number by powers of 5. If it results in more than 1 then the number of trailing zeros will be the number of 5s. Add this to count.
Take an integer number as input.
Function trailing_zeros(int number) takes number and returns the count of trailing zeroes in factorial of number.
Take the initial count as 0.
Using a for loop, divide the number by powers of 5.
If number/i is greater than 1, add this value to count.
Return count as result at the end of loop.
Example
#include <iostream>
using namespace std;
int trailing_zeros(int number){
int count = 0;
for (int i = 5; number / i >= 1; i *= 5){
int temp = number / i;
count = count + temp;
}
return count;
}
int main(){
int number = 50;
cout<<"Count of trailing zeros in factorial of a number are: "<<trailing_zeros(number);
return 0;
}Output
If we run the above code it will generate the following output −
Count of trailing zeros in factorial of a number are: 12
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