Prime Factoring Calculator for Primes Factorization of a Number This calculator will save a lot of time and tedium by finding factors for any number less than or equal to 10,000 with the click of a button (may accommodate numbers as high as 1 million -- depending on the number entered -- and calculator will show its work so you can check to make sure the factorization was completed).

Plus the prime factoring calculator will simplify the list of prime numbers found into an exponential expression.

If you would like to see if a number is prime before attempting to factor it, please visit the prime number checker.

Or, if you wish to generate a customizable, printable list of primes, please visit the prime number generator.

Prime Factoring Calculator

Find all prime factors of a number and simplify the result into an exponential expression.

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Number:Number:Number to factor:Number to find factors for:

Number:

Enter the number you would like the prime factorization calculator to find the primes for (maximum of 1 million). Note that the factorization of numbers larger than 10,000 may not be completed, however the prime factoring calculator will show its work so you can check to make sure.

 # Number to find factors for
# primes:Number of primes:Number of prime factors:Number of prime factors:

Number of prime factors:

This is how many prime numbers were found to be factors of the entered number.

Prime list:Prime number list:Prime number list:Prime number list:

Prime number list:

This is the list of prime numbers found to be factors of the entered number. Just beneath the list you will see the simplified primes format, along with the series of multiplications that checks to make sure the factorization was calculated correctly (numbers greater than 10,000 may be too large to complete the factorization).

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Related Calculators Learn

What prime numbers are and how to manually perform prime number factoring.

What Are Prime Numbers?

Prime number definition: Any number greater than 1 that is only divisible by 1 and the number itself. For example, the number 11 is a prime number because no number other than 1 and 11 can be divided into 11 evenly (no remainder). Note that primes are also referred to as natural numbers.

The number 12, on the other hand, is not a prime number because it can be divided evenly by factors 1, 2, 3, 4, 6, and 12. This and other non-primes are also referred to as composite numbers.

How to Manually Find Prime Factors of a Number

If you didn't have access to the handy prime factorization web app on this site, the manual primes factorization of a number can be tedious and time-consuming.

To illustrate the manual primes factoring of say, the number 24, you will first need a prime numbers list to refer to. Here is a list of all primes under 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Next, using upside-down long division and starting with the smallest of the primes and working your way up, you begin a series of divisions until the quotient is equal to 1, like this:

 2 24 2 12 2 6 3 3

Prime Factorization of 24 = 2 x 2 x 2 x 3

Using a rule of exponents, xa * xb = x(a + b), the above list of prime numbers found for the number 24 can then be simplified into the following exponential expression:

23 * 3

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".