# How to Calculate Prime Factors

**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: http://www.webinfocentral.com/MATH/Factorization.aspx

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: http://www.webinfocentral.com/MATH/Factorization.aspx

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*

## Comments

I prefer the Wolfram Alpha factorizer, much faster and handles larger numbers. And this Gaussian prime factorizer, breaks down integers even further http://www.had2know.com/academics/gaussian-prime-f...