freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-383-divisibility-comparison-between-factorials.md

---
id: 5900f4ed1000cf542c50ffff
title: 'Problem 383: Divisibility comparison between factorials'
challengeType: 5
forumTopicId: 302047
dashedName: problem-383-divisibility-comparison-between-factorials
---

# --description--

Let f5(n) be the largest integer x for which 5x divides n.

For example, f5(625000) = 7.

Let T5(n) be the number of integers i which satisfy f5((2·i-1)!) &lt; 2·f5(i!) and 1 ≤ i ≤ n. It can be verified that T5(103) = 68 and T5(109) = 2408210.

Find T5(1018).

# --hints--

`euler383()` should return 22173624649806.

```js
assert.strictEqual(euler383(), 22173624649806);
```

# --seed--

## --seed-contents--

```js
function euler383() {

  return true;
}

euler383();
```

# --solutions--

```js
// solution required
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`
			`id: 5900f4ed1000cf542c50ffff`
			`title: 'Problem 383: Divisibility comparison between factorials'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 09:17:33 -07:00			`forumTopicId: 302047`
feat(curriculum): restore seed + solution to Chinese (#40683) * feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com> 2021-01-13 03:31:00 +01:00			`dashedName: problem-383-divisibility-comparison-between-factorials`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --description--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`Let f5(n) be the largest integer x for which 5x divides n.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`For example, f5(625000) = 7.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`Let T5(n) be the number of integers i which satisfy f5((2·i-1)!) < 2·f5(i!) and 1 ≤ i ≤ n. It can be verified that T5(103) = 68 and T5(109) = 2408210.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			`Find T5(1018).`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --hints--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`euler383()` should return 22173624649806.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			```js
			`assert.strictEqual(euler383(), 22173624649806);`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`function euler383() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 09:57:40 -07:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`return true;`
			`}`

			`euler383();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`// solution required`
			```