Factorial factorization

This function calculates the factorization of the given number's factorial.

int factors(int num)
{
    int i,tmp,cnt;
    
    for(i=0;i<max_prime && prime[i]<=num;i++)
    {
        cnt=0;
        tmp=num;
        cout<< prime[i] << " ";
        while(tmp>0)
        {
            cnt+=floor(tmp/prime[i]);
            tmp/=prime[i];
        }
        cout<< cnt << endl;
    }
}

Last non-zero digit of factorial

To find the last non-zero digit of a factorial number, the idea is to remove the extra zeroes in every step multiplying the numbers and don't need to hold the whole big number, just a small digit numbers from the last non-zero digits.
Here goes the code-

#include<stdio.h>
int main()
{
    long long int ans;
        int num;
        scanf("%d",&num);
 
        ans=1;
        for(int i=2;i<=num;i++)
        {
                ans=ans*i;
 
                while(ans%10==0)
                {
                        ans/=10;
                }
                ans%=10000000;
        }
        printf("%lld\n",ans%10);
 
        return 0;
}

Trailing zero in factorial

Finding number of trailing zero in factorial-

#include <stdio.h>
int main()
{
	int n,total,deno;
        scanf("%d",&n);
		
	total=0;
	deno=5;
	while(deno<=n)
	{
		total+=n/deno;
		deno*=5;
	}
	printf("%d\n",total);

	return 0;
}

Number of digits in factorial

This program calculate how many digit in factorial of the number in given base
Anyone can just calculate number of digits in decimal, then b=10 always.

#include <stdio.h>
#include <math.h>
int main()
{
	int number,i,base,digit;
	double c,a=0;

	printf("Give the base and the number: ");
	scanf ("%d%d",&base,&number);

	c=log10(base);
	for (i=number;i>=1;i--) {

		a+=(log10(i))/c; 
	}
	digit=a+1;
	printf ("%d\n",digit);

	return 0;
}