---
id: 5a23c84252665b21eecc7eec
title: Long multiplication
challengeType: 5
---

## Description
<section id='description'>
Explicitly implement  <a href="https://en.wikipedia.org/wiki/long multiplication">long multiplication</a>.
This is one possible approach to arbitrary-precision integer algebra.
</section>

## Instructions
<section id='instructions'>
Write a function that takes two strings of large numbers as parameters. Your function should return the product of these two large numbers as a string.
<strong>Note:</strong> In JavaScript, arithmetic operations are inaccurate with large numbers, so you will have to implement precise multiplication yourself.
</section>

## Tests
<section id='tests'>

``` yml
tests:
  - text: <code>mult</code> should be a function.
    testString: assert(typeof mult == 'function', '<code>mult</code> should be a function.');
  - text: <code>mult("18446744073709551616", "18446744073709551616")</code> should return a string.
    testString: assert(typeof mult("18446744073709551616", "18446744073709551616") == 'string', '<code>mult("18446744073709551616", "18446744073709551616")</code> should return a string.');
  - text: <code>mult("18446744073709551616", "18446744073709551616")</code> should return <code>"340282366920938463463374607431768211456"</code>.
    testString: assert.equal(mult("18446744073709551616", "18446744073709551616"), "340282366920938463463374607431768211456", '<code>mult("18446744073709551616", "18446744073709551616")</code> should return <code>"340282366920938463463374607431768211456"</code>.');
  - text: <code>mult("31844674073709551616", "1844674407309551616")</code> should return <code>"58743055272886011737990786529368211456"</code>.
    testString: assert.equal(mult("31844674073709551616", "1844674407309551616"), "58743055272886011737990786529368211456", '<code>mult("31844674073709551616", "1844674407309551616")</code> should return <code>"58743055272886011737990786529368211456"</code>.');
  - text: <code>mult("1846744073709551616", "44844644073709551616")</code> should return <code>"82816580680737279241781007431768211456"</code>.
    testString: assert.equal(mult("1846744073709551616", "44844644073709551616"), "82816580680737279241781007431768211456", '<code>mult("1846744073709551616", "44844644073709551616")</code> should return <code>"82816580680737279241781007431768211456"</code>.');
  - text: <code>mult("1844674407370951616", "1844674407709551616")</code> should return <code>"3402823669833978308014392742590611456"</code>.
    testString: assert.equal(mult("1844674407370951616", "1844674407709551616"), "3402823669833978308014392742590611456", '<code>mult("1844674407370951616", "1844674407709551616")</code> should return <code>"3402823669833978308014392742590611456"</code>.');
  - text: <code>mult("2844674407370951616", "1844674407370955616")</code> should return <code>"5247498076580334548376218009219475456"</code>.
    testString: assert.equal(mult("2844674407370951616", "1844674407370955616"), "5247498076580334548376218009219475456", '<code>mult("2844674407370951616", "1844674407370955616")</code> should return <code>"5247498076580334548376218009219475456"</code>.');
```

</section>

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

<div id='js-seed'>

```js
function mult(strNum1, strNum2) {
  // Good luck!
}
```

</div>

</section>

## Solution
<section id='solution'>

```js
function mult(strNum1, strNum2) {
    var a1 = strNum1.split("").reverse();
    var a2 = strNum2.toString().split("").reverse();
    var aResult = new Array;

    for ( var iterNum1 = 0; iterNum1 < a1.length; iterNum1++ ) {
        for ( var iterNum2 = 0; iterNum2 < a2.length; iterNum2++ ) {
            var idxIter = iterNum1 + iterNum2;    // Get the current array position.
            aResult[idxIter] = a1[iterNum1] * a2[iterNum2] + ( idxIter >= aResult.length ? 0 : aResult[idxIter] );

            if ( aResult[idxIter] > 9 ) {    // Carrying
                aResult[idxIter + 1] = Math.floor( aResult[idxIter] / 10 ) + ( idxIter + 1 >= aResult.length ? 0 : aResult[idxIter + 1] );
                aResult[idxIter] %= 10;
            }
        }
    }
    return aResult.reverse().join("");
}
```

</section>