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Cover image for Did you know that 70! (factorial of 70) is bigger than a googol?

Did you know that 70! (factorial of 70) is bigger than a googol?

codeguppy profile image Adrian ・2 min read

Did you know that 70! (factorial of 70) is bigger than a googol?

A googol is the number 10 followed by 100 zeros. This number is so big that some researchers believe is bigger than the number of atoms in the Universe.

... and still 70! is bigger than a googol !!!

The big number googol attracted also the attention of the Google founders... who picked the name Google (based on “googol”) to signify that the search engine provides large quantities of information.

Understanding numbers and how big or small they are is an important aspect of daily programming. This is essential for selection of the proper architecture or choosing right type of data structures.

As a fun exercise, try to calculate 70! in your favorite language. Don't use any fancy BigNumber type structures... instead do all the calculations using only primitive types.

Below is a JavaScript solution from the codeguppy.com website. To run the solution outside codeguppy.com, just replace 'println' with 'console.log'

For your convenience the code is also provided in this playground.

// Coding challenge #53. Calculate all the digits of 70! (factorial of 70)
// Playground: https://codeguppy.com/code.html?m4AfgJmCABGNEvKlUNtM

println(factorial(70));

// Calculate factorial(n) ... using big number calculations
function factorial(n)
{
    var prod = "1";

    for(var i = 2; i <= n; i++)
    {
        prod = mult(prod, i.toString());
    }

    return prod;
}

// Multiplies sNumber1 * sNumber2
// Each number is provided as string
function mult(sNumber1, sNumber2)
{
    // Calculate partial results according to multiplication algorithm
    var partialResults = [];

    for(var i = sNumber2.length - 1; i >= 0; i--)
    {
        var digit = parseInt(sNumber2[i]);

        var partialResult = multDigit(sNumber1, digit);
        partialResult += "0".repeat(partialResults.length);

        partialResults.push(partialResult);
    }

    // Sum partial results to obtain the product
    var sum = "";

    for(var r of partialResults)
    {
        sum = add(sum, r);
    }

    return sum;
}

// Multiplies number sNumber (as string) with a single digit number
function multDigit(sNumber, digit)
{
    var p = "";
    var carry = 0;

    for(var i = sNumber.length - 1; i >= 0; i--)
    {
        var numberDigit = parseInt(sNumber[i]);

        var prod = digit * numberDigit + carry;
        var prodDigit = prod % 10;
        carry = Math.floor(prod / 10);

        p = prodDigit.toString() + p;
    }

    if (carry > 0)
        p = carry + p;

    return p;
}


function add(sNumber1, sNumber2)
{
    var maxSize = Math.max(sNumber1.length, sNumber2.length);

    var s1 = sNumber1.padStart(maxSize, "0");
    var s2 = sNumber2.padStart(maxSize, "0");

    var s = "";
    var carry = 0;

    for(var i = maxSize - 1; i >= 0; i--)
    {
        var digit1 = parseInt(s1[i]);
        var digit2 = parseInt(s2[i]);

        var sum = digit1 + digit2 + carry;
        var digitSum = sum % 10;
        carry = sum >= 10 ? 1 : 0;

        s = digitSum.toString() + s;
    }

    if (carry > 0)
        s = carry + s;

    return s;
}

Happy coding ... and don't forget to visit codeguppy.com for more fun activities. You can also follow @codeguppy on Twitter and other social networks.

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