---
id: 5900f4381000cf542c50ff4b
title: 'Problem 204: Generalised Hamming Numbers'
challengeType: 5
forumTopicId: 301845
dashedName: problem-204-generalised-hamming-numbers
---

# --description--

A Hamming number is a positive number which has no prime factor larger than 5.

So the first few Hamming numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15.

There are 1105 Hamming numbers not exceeding ${10}^8$.

We will call a positive number a generalised Hamming number of type $n$, if it has no prime factor larger than $n$. Hence the Hamming numbers are the generalised Hamming numbers of type 5.

How many generalised Hamming numbers of type 100 are there which don't exceed ${10}^9$?

# --hints--

`generalisedHammingNumbers()` should return `2944730`.

```js
assert.strictEqual(generalisedHammingNumbers(), 2944730);
```

# --seed--

## --seed-contents--

```js
function generalisedHammingNumbers() {

  return true;
}

generalisedHammingNumbers();
```

# --solutions--

```js
// solution required
```
