---
id: 5900f3b41000cf542c50fec7
challengeType: 5
title: 'Problem 72: Counting fractions'
forumTopicId: 302185
---

## Description
<section id='description'>

Consider the fraction, <var>n</var>/<var>d</var>, where n and d are positive integers. If <var>n</var><<var>d</var> and HCF(<var>n</var>,<var>d</var>)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for <var>d</var> ≤ 8 in ascending order of size, we get:

<div style='text-align: center;'>1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8</div>

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for <var>d</var> ≤ 1,000,000?

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>countingFractions()</code> should return a number.
    testString: assert(typeof countingFractions() === 'number');
  - text: <code>countingFractions()</code> should return 303963552391.
    testString: assert.strictEqual(countingFractions(), 303963552391);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function countingFractions() {

  return true;
}

countingFractions();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>