Determine Number of Trailing Zeros of a Factorial Function (javascript)

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I'm writing a function that returns the number of trailing zeros of a factorial. It seems that the amount of zeros increases from 0! for every 5 positive increments, but also increases 1 zero for every 25 increments. The problem is that when I pass in a number like 1000, it should return 249, but it returns 240 instead. Am I missing something?

I'm almost positive there is a better way to write this, but hopefully, someone can tell me what I'm missing in my current function?

Note: This function must not calculate the actual factorial to determine the number of trailing zeros.

function zeros(n) {
  const extraZeros = n/25
  const zeros = n/5
  if(extraZeros >= 1) {
    return zeros + Math.floor(extraZeros)
  }else{
    return Math.floor(zeros)
  }
}
console.log(zeros(0), 0);
console.log(zeros(5), 1);
console.log(zeros(6), 1);
console.log(zeros(30), 7);
console.log(zeros(60), 14);
console.log(zeros(1000), 249); // missing 9 zeros?

Any help would be greatly appreciated, Thank you!

javascript
1 Answers

It seems that the amount of zeros increases from 0! for every 5 positive increments, but also increases 1 zero for every 25 increments.

You're right, but read this sentence again. Do you see the pattern?

It'll also increase a zero for every 125 and 625 increments, etc. You need to generalize based on powers of 5.

const zeros = (n) => {
  let power = 1;
  let totalZeros = 0;
  while (n > 5 ** power) {
    totalZeros += Math.floor(n / (5 ** power));
    power++;
  }
  return totalZeros;
};
console.log(zeros(0), 0);
console.log(zeros(5), 1);
console.log(zeros(6), 1);
console.log(zeros(30), 7);
console.log(zeros(60), 14);
console.log(zeros(1000), 249);

Another way of writing it, from Patrick Roberts:

const zeros = (n) => {
  let totalZeros = 0;
  for (let power = 5; power < n; power *= 5) {
    totalZeros += Math.floor(n / power);
  }
  return totalZeros;
};
console.log(zeros(0), 0);
console.log(zeros(5), 1);
console.log(zeros(6), 1);
console.log(zeros(30), 7);
console.log(zeros(60), 14);
console.log(zeros(1000), 249);

user_95152070
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