51nod_1003 factorial 0 of the number (5 in the n!, number theory)

Test instructions

How many 0 are behind the factorial of n? The factorial of 6 = 1*2*3*4*5*6 = 720,720 is followed by a 0. Input

A number n (1 <= n <= 10^9)

OutPut

Number of outputs 0

Ideas:

A 0 can only be obtained by 2*5. Statistics n! the number of 2 and the number of 5, take less. That is, the number of 5 in n! is obtained. "Number theory: [n/5]+[n/5^2]+[n/5^3]+[n/5^4]+ ...]" {I can also draw this conclusion from my own analysis}

Code:

int Main () {    int  n;     >> N;    ll ans=0;    ll tmp=5;      while (tmp<=N) {        ans+ = (n/tmp);        TMP*=5;    }    Print ("%lld\n", ans);         0 ;}

51nod_1003 factorial 0 of the number (5 in the n!, number theory)