A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers. Examples of numbers which aren't prime are 4, 6, and 12 to pick a few.
If we totally factor a number into positive prime factors there only will be one way of doing it. That is the cause for factoring things in this way. For above example of 12 the complete factorization will be,
12 = ( 2) ( 2) (3)