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:
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:
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: