Prime factorization is a method of reducing a number into its prime factors.
Prime factorization is made up of two words prime and factorization, in which prime implies all the prime numbers and factorization implies all the factors.
Hence, by combining these two words, we get prime factorization as the equivalent for getting prime factors of a number.

Prime factors are those numbers which are the basis for further arithmetic study. Any number in the field of mathematics can either be prime or composite but not both.
The method of reducing any given number into the product of its prime is known as the method of factoring.
It is very interesting to note that any composite number can also be reduced into prime factors.
We will now define the concept of prime factorization in detail by defining the following terms:
Definition of Prime Numbers: A prime number is any whole number greater than 1, which can be divided only by two numbers which are:
1).    The number itself and
2).    The number 1.
Prime numbers starts from 2, 3, 5, 7, 11, 13, 17 and so on. Note that the smallest prime number is 2 which is an even number and rest all of the prime numbers are all odd numbers.

Definition of Factors of a Number: Factors are those numbers which when multiplied by each other give us another number, as can be seen from the following numbers which are factors of 6:
Factors of a Number
Note that 2 and 3 are factors of 6, as when multiplied with each other give us 6.

Now we can define the meaning of prime factorization, which is as follows:
Prime Factorization Definition: Prime factorization is a method of finding all the prime numbers which when multiplied with each other gives us the result of the original number given, whose factors are to be found.Note that each and every number greater than 1, can be expressed as the product of prime factors and hence, prime factorization is a method of reducing any number into its product of prime factors.