Prime Factorization and Factors

A factor of a given number is called a Prime factor if this factor is a Prime number

Prime factorization is expressing a number as a product of its Prime factors

When two or more numbers are multiplied, each number is called factor of the product

Prime number has two unique factors - 1 and the number itself
For example: 3
As 3 = 3 x 1 so 3 has only two factors - 1 and the number itself (3)

Composite number has more than 2 factors.
For example: 4

4 = 4 x 1 = 2 x 2 x 1.

4 has more than two factors, that is, 1, 2 and 4.
So, 4 is a composite number

1 and 0 are neither Prime nor Composite

A factor of a given number is a Prime factor if this factor is a Prime number

Prime Factorization is expressing a number as a product of its Prime factors.
For example, we can express 4 as product of primes as follows:

4 = 4 x 1 = 2 x 2 x 1

Remember that every Composite number can be factorized into Primes in only one way except for the order of Primes.

For example:

4 = 4 x 1 = 2 x 2 x 1
Or,

4 = 1 x 4 = 1 x 2 x 2

Only the order of primes is different but primes are same