ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

How to Calculate Prime Factors

Updated on September 4, 2009
Online Prime Factors Calculator:
Online Prime Factors Calculator:

FACTORING (a.k.a. Factorization) and PRIME NUMBERS (or simply Primes) are the centerpiece of Number Theory.

FACTORING of the Integer number is a mathematical procedure of extracting all of its Prime Divisors, also called Factors.

PRIME NUMBERS are the Integers, which have only two trivial divisors: 1 and the number itself. Any Integer except for Primes is called Composite Number; it contains at least one non-trivial divisor (factor).Any Integer number could be presented as a Product of its Factors. Factorization example is shown below:

12 = 2 * 2 * 3,

where 2 and 3 are Prime Numbers.

Below is the list of 25 Prime Numbers in the range 1…100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,69, 71, 73, 79, 83, 97

Trivial divisor 1 is excluded from the list: by convention, it is not considered a Prime Number.

Practical Factorization of any Integer Number, containing up to 19 decimal digits could be performed online using free Factorization Calculator, compatible with all major Web Browsers (available at:

To Factorize the Integer using online Factorization Calculator enter the number into the text box and click on the "=" screen button. You will see the number presented as the Product of its Prime divisors; number 1 as a trivial divisor is excluded from the list.

Primality test, in other words, the test intended to find out that the Integer number is actually a Prime, could be performed in the same way as Factoring: enter the Integer number and calculate the Factor(s): if resulted list contains only one Factor, then the number is Prime and vice versa.

Primality test and Factorization of the large Integers is not a trivial task, and sometimes requires substantial amount of time to complete. For example, the Integer number 324632623645234523, which is actually a Prime could take up to 10 sec to calculate. As per the definition, result will contain just a single divisor – the number itself (trivial divisor 1 is implied and, thus, omitted from the list).

For faster Primality check, it could be performed without full Factoring. It’s sufficient to find the first non-trivial divisor to claim that the Integer under the test is not a Prime, thus avoiding the further Factoring. This concept is implemented in the fast Primality testing algorithm, which could be run separately from full Factoring, thus providing some speed benefits. It’s recommended to perform the Primality test of Integer Number first and proceed to the Factorization only the test failed, in other words, if the Number is composite, thus containing more than one non-trivial Factor.
In order to Check the Primality and perform the Factorization follow the steps outlined below:

1. Open the Web Browser and navigate to the Prime and Factorization Calculator page at:

2. Enter the Integer Number and click on the button "IsPrime" located at the top of the panel.

3. If the answer is “true”, then you do not need further Factorization; by definition, Prime Numbers contains only two trivial divisors: 1 and the number itself. Otherwise, proceed to the next step.

4. Click on the screen button marked as “=” to Factorize the Integer Number and get the list of all its Prime Factors, displayed to the right of the button.

Copyright© 2009 Alexander Bell


    0 of 8192 characters used
    Post Comment


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)