Before factorization, we need to know that what the factor is...?
Example: The number 2 divides the number 4, therefore 2 is a factor of 4.
The number 3, divides the number 12, therefore 3 is a factor of 12.
Factorization means when we write a number as a product of smaller numbers or the method to breaking down a number into smaller numbers.
Example: The number 20 can be written as the product of smaller numbers as,
\(20=4\times5\),
\(20=2\times10\)
\(20=2\times2\times5\)
So, the numbers 2,4,5 and 10 are the factors of 20.
Prime factorization: This is a method to find which prime numbers multiply together to make the original number.
Example: Suppose we need to find prime factors of 20. 
Start dividing 20 with the smallest prime number which is 2,
we will get \(\frac{20}{2}=10\),
so 20 can be written as \(2\times10\)
But 10 is not a prime number,
Now divide 10 with the smallest prime number, we will get \(\frac{10}{2}=5\),
so 10 can be written as \(2\times5\).
Now 5 is a prime number means we can not divide it further, so by combining these we can say that:
20 can be written as the product of prime numbers 2,2 and 5, these are the prime factors of 20 as:
\(\mathbf{20}=\mathbf{2}\times\mathbf{2}\times\mathbf{5}\)
Another method to find Prime Factors is Factor Tree
Factor tree: This method includes to find any factors of given number and then find factors of those factors till we didn’t get all the prime numbers.
Example: Suppose we need to find prime factors of 108 by using factor tree method.
Take factors of \(108\ =\mathbf{9}\times\mathbf{12}\) and write under 108 
Now find the factors of factors 9 and 12 (which we got in step 1), as:
\(9=\mathbf{3}\times\mathbf{3}\\) and
12=\mathbf{4}\times\mathbf{3}\),
write factors under the numbers 9 and 12.
now 3 is a prime number but not 4, so find factors of 4, as:
4=2\times2
Now we got all the prime factors of 108 as:
\(\mathbf{2}\times\mathbf{2}\times\mathbf{3}\times\mathbf{3}\times\mathbf{3}\)
So, \(\ \mathbf{108}=\mathbf{2}\times\mathbf{2}\times\mathbf{3}\times\mathbf{3}\times\mathbf{3}\)