0's of a factorial

I want to make a program which takes a number n and then outputs how many 0's the factorial has on the right site of the factorial.

For this, I thought about the following algorithm:
I noticed, every 5th number gets a 0 more. So, 1->0,5->1,10->2 and so on.

In this program I divide the number by 5 and subtract its modulo to it:

#include <iostream>

int main(){
    int casos;
    std::cin>>casos;
    int num=0;
    long result;
    for(int n =0;n<casos;n++){
        result=0;
    std::cin>>num;    
    result=(num-num%5)/5;
    if(num==0){
        result=1;
    }
    std::cout<<result<<"\n";    
    }
    return 0;
}

Ganado (6811)

So, what exactly is your question?

BTW: https://oeis.org/A027868

yabi2943993 (59)

The program does not work... The checker invalids it

Ganado (6811)

Well, the most obvious thing is that 0! is 1, which has 0 zeroes.

yabi2943993 (59)

The problem indicates, that the result has to be 1 if the num equals 0.

Además, por convenio, el factorial de 0 es 1 (es decir, 0! = 1).

I don't know if that means just the factorials or also the 0's. But the checker does not validate it even without the 0 part

Last edited on

Ganado (6811)

That isn't what that is saying. You're still trying to calculate the number of trailing 0s. 0! (1) has zero trailing 0s.

Look at the link I posted. Compare your results to the sequence.
hint: 25!

Moral of the story: Patterns with early numbers don't always last forever.

Last edited on

yabi2943993 (59)

Ok. But the program does not work also if 0 has 0 0's

jonnin (11437)

doesn't matter if it works for anything, the math is wrong.
when you do 100!, *100 immediately adds 2 zeros. when you do 1000!, it immediately adds 3 zeros. And so on. if you are only doing to 99! or less, then you may be able to fit a partial pattern, but if you are only doing to 99 or less, just dump the answer in a lookup table.

lastchance (6980)

@yabi2943993,

You do know that @dutch gave you the exact solution and code here:
http://www.cplusplus.com/forum/general/267490/#msg1150931

As @jonnin said: your maths is wrong. There are more increments than simply increasing by 1 every multiple of 5.

0's of a factorial

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