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.
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 nonprimes are also referred to as composite numbers.
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:
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 
Using a rule of exponents, x^{a} * x^{b} = x^{(a + b)}, the above list of prime numbers found for the number 24 can then be simplified into the following exponential expression:
With that, let's use the Prime Factoring Calculator to find all prime factors of a given number.

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