Simply break down the number into a product of prime numbers (its prime factors)

Examples:
• the prime factorization of 3 = 3
• the prime factorization of 22 = 11 × 2
• the prime factorization of 11,101 = 17 × 653

Examples of incorrect prime factorization
•  44 = 11 × 4 is not correct. Prime factorization requires that all of the factors are prime numbers, and 4 is not prime. Therefore, this is not an example of prime factorization of number.
•  44 = 22 × 2 is not correct. Prime factorization requires that all of the factors are prime numbers, and 22 is not prime. Therefore, this  is not an example of prime factorization of number.

How to determine if a Number is Prime

To determine whether or not a number is prime all that you have to do is find any integer that evenly divides the number in question (not counting 1 and the given number). Use Math Warehouse's Calculator to determine if any number is prime.

Also, you only need to check up to the square root of a number to see if it is prime. Consider the number 15, for example. If we want to know if is is prime or not,
we first check to see if 2 evenly divides it, and, of course, 2 does not go into 15 so..let's
check to see if 3 evenly divides it, and of course 3 does go into . Now, notice that we also, at this point have checked if 5 goes into the number because 3* 5 = 15. This is why you only have to check up to the square root of a given number, let's call that number x, when you are trying to determine if it is prime. After the square root,you are just checking the other pair of factors, the the numbers that are like the '5' in prior example and that had already been checked by all the numbers less than or equal to the square root of the number (ie the '2' and '3' in the example).