Prime numbers are the integers (i.e., whole numbers), which have two and only two trivial divisors, namely: 1 and the number itself. As per definition, number 1 is not considered a prime number. Any integer, which is not a prime number, is called a composite number; it contains at least one non-trivial divisor (also referred as factor).
Prime factorization (a.k.a. prime factoring) is a mathematical procedure of extracting all prime divisors (factors) from integer numbers.
Primality test is the mathematical procedure intended to prove or disprove that the integer number under the test is actually a prime number. Primality test could be performed by means of prime factoring: if result contains only trivial factors then the number is a prime and vice versa.
Any integer number could be presented as a product of its prime factors. Prime factorization examples and corresponding primality checks are shown below:
2 = 1 * 2 (2 is a prime number, containing only trivial divisors)
3 = 1 * 3 (3 is a prime number, containing only trivial divisors)
6 = 2 * 3 (6 is a composite number, containing non-trivial prime divisors 2 and 3)
Following is the list of 25 prime numbers existing in the range of 1 thru 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
Online prime factorization calculator
Prime factorization of any Integer number of to 19 decimal digits could be performed online using free online Prime Factorization Calculator. There is also a version of Mobile Prime Factorization Calculator, customized for the small-screen portable devices with internet connectivity, such as Apple iPod Touch, iPhone and Microsoft Zune HD. Both online prime factorization calculators demonstrate exceptional accuracy and computational power: for example, the primality test of integer number 324632623645234523, which takes about 5 sec to calculate online could last for minutes or hours if performed on any hand-held programmable calculators.
Prime factorization of large integers in general is not a trivial task, and sometimes requires substantial amount of time to complete. For faster primality check, it could be performed without complete factoring; it’s sufficient to find just the first non-trivial divisor to prove that the integer number under the test is not a prime, thus omitting the rest of factoring procedure. This concept is implemented in the fast primality test algorithm, also available at the same page.
Practical steps to perform the prime factorization online are outlined below:
- Open web browser and navigate it to the Prime Factorization Calculator: http://www.webinfocentral.com/MATH/Factorization.aspx
- Enter any integer number up to 19 digits and click the button "IsPrime" located at the top of the page.
- If the answer is “true”, then you do not need factorization; by definition, prime numbers contains only two trivial divisors: 1 and the number itself. Otherwise, proceed to the next step.
- Click on the screen button marked as “=” to perform the prime factorization: the list of all non-trivial prime factors is displayed to the right of the button.
- To perform the Prime Factorization on the mobile devices (like Apple iPod Touch, iPhone, Microsoft Zune HD, Smart Phones) use the free online Mobile Factorization Calculator available at: http://www.webinfocentral.com/Mobile/Factoring.aspx
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