Prime factorization means to write a number as product of its prime factors, i.e. as a product of prime numbers.
What is a prime factorization?
A prime factorization is writing your number as a product of prime numbers. E.g. 12 can be written as 2*2*3 or 16 can be written as 2*2*2*2. The prime numbers are called prime factors. The prime factorization of a number is unique.
How to do a prime factorization?
Simply find out by which numbers a prime number is divisible. If the number is divisible by a prime number, write it as a product of a prime number and another number and continue. If it is not divisible by any prime number, it must be a prime number itself.
For example let's do the prime factorization of 48.
First check out if 48 is divisible by 2. Yes, it is, and 48=2*24. And we see that 24 is also divisible by 2 and 24=2*12, which means 48=2*2*12. Furthermore, we see that 48=2*2*2*6 or 48=2*2*2*2*3. Now 3 is also a prime number, which means we are done.
Another example: prime factorization of 18.
18=2*9. 9 is not divisible by 2, but by 3, and 9=3*3, so 18=2*3*3.
Just enter any number and it will be decomposed into prime factors.