---
id: 5900f4151000cf542c50ff27
title: 'Problem 168: Number Rotations'
challengeType: 5
forumTopicId: 301802
dashedName: problem-168-number-rotations
---

# --description--

Consider the number 142857. We can right-rotate this number by moving the last digit (7) to the front of it, giving us 714285.

It can be verified that $714285 = 5 × 142857$.

This demonstrates an unusual property of 142857: it is a divisor of its right-rotation.

Find the last 5 digits of the sum of all integers $n$, $10 < n < 10100$, that have this property.

# --hints--

`numberRotations()` should return `59206`.

```js
assert.strictEqual(numberRotations(), 59206);
```

# --seed--

## --seed-contents--

```js
function numberRotations() {

  return true;
}

numberRotations();
```

# --solutions--

```js
// solution required
```