freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-3-largest-prime-factor.english.md

---
id: 5900f36f1000cf542c50fe82
challengeType: 5
isHidden: false
title: 'Problem 3: Largest prime factor'
forumTopicId: 301952
---

## Description
<section id='description'>

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the given `number`?

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>largestPrimeFactor(2)</code> should return a number.
    testString: assert(typeof largestPrimeFactor(2) === 'number');
  - text: <code>largestPrimeFactor(2)</code> should return 2.
    testString: assert.strictEqual(largestPrimeFactor(2), 2);
  - text: <code>largestPrimeFactor(3)</code> should return 3.
    testString: assert.strictEqual(largestPrimeFactor(3), 3);
  - text: <code>largestPrimeFactor(5)</code> should return 5.
    testString: assert.strictEqual(largestPrimeFactor(5), 5);
  - text: <code>largestPrimeFactor(7)</code> should return 7.
    testString: assert.strictEqual(largestPrimeFactor(7), 7);
  - text: <code>largestPrimeFactor(8)</code> should return 2.
    testString: assert.strictEqual(largestPrimeFactor(8), 2);
  - text: <code>largestPrimeFactor(13195)</code> should return 29.
    testString: assert.strictEqual(largestPrimeFactor(13195), 29);
  - text: <code>largestPrimeFactor(600851475143)</code> should return 6857.
    testString: assert.strictEqual(largestPrimeFactor(600851475143), 6857);

```

</section>

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

<div id='js-seed'>

```js
function largestPrimeFactor(number) {
  // Good luck!
  return true;
}

largestPrimeFactor(13195);
```

</div>



</section>

## Solution
<section id='solution'>


```js
const largestPrimeFactor = (number) => {
  let largestFactor = number;

  for (let i = 2; i <= Math.sqrt(largestFactor); i++) {
    if (!(largestFactor % i)) {
      let factor = largestFactor / i;
      let candidate = largestPrimeFactor(factor);

      return i > candidate ? i : candidate;
    }
  }

  return largestFactor;
}
```

</section>