Prime Factoring Calculator for
Primes Factorization of a Number

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The prime factoring calculator on this page will quickly generate a list of all primes found to be factors of a number.

This free online calculator will save a lot of time and tedium by finding factors for any number that is 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 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 primes list generator.

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 prime number because it can be divided evenly by the 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 calculator below, 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

With that, let's use the Prime Factoring Calculator to find all prime factors of a given number.

Prime Factoring Calculator
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Instructions: Enter the number you would like to calculate the prime factorization for, then click the "Begin Factoring Prime Numbers" button.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Prime Factoring Calculator.

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Prime Factoring Calculator Glossary of Terms

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Prime Number: Also called a natural number, can be defined as any number greater than 1 that is only divisible by the number 1 and the number itself.

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

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).

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