I am not sure why I am getting a TLE for codechef

Question

When I submit my solution to codechef, I keep getting a time limit error. I switched to buffered reader from scanner, but that did not fix it. I'm thinking it is in my algorithm, but I am not sure where, other than checking each 5 decrement could be unnecessary. Where is the issue I am having located so that I can figure out how to solve it?

Here is the link for reference: https://www.codechef.com/problems/FCTRL

Here is my code:

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

class Factorial {
    public static void main(String[] args) throws IOException {
        BufferedReader keyboard = new BufferedReader(new InputStreamReader(System.in));

        //how many numbers follow
        int number = Integer.parseInt(keyboard.readLine());
        //stores zSum's to output later
        int[] answerArray = new int[number];

        for(int i = 0; i < number; i++) {
            //the number to compute factorial
            int n = Integer.parseInt(keyboard.readLine());

            // moves number to one ending in 5
            n -= n % 5;
            //stores number of zeros
            int zSum = 0;

            for (int j = n; j > 0; j -= 5) {

                //if a power of 5, add 1 to zSum
                for (int k = 5; k <= j; k *= 5) {
                    if (j % k == 0) {
                        zSum ++;
                    }
                }
            }
            answerArray[i] = zSum;
        }

        //println all values in array
        for (int i = 0; i < number; i++) {
            System.out.println(answerArray[i]);
        }
    }
}

Answer 1

Your complexity is to high,

for (int j = n; j > 0; j -= 5)

will do O(N) operations. Inner cycle will add log to complexity. You should write use some other approach. It can be done using O(log(N)) time for each testcase.