PRIME FACTORS AND PRIME FACTORIZATION

PRIME FACTORS AND PRIME FACTORIZATION

Recall that a prime number is a number greater than 1 and having no factors except 1 and itself

Prime Factors

The factors of 12 are: 1, 2, 3, 4, 6, and 12 of which only 2 and 3 are prime numbers. Prime numbers 2 and 3 are said to be prime factors of 12

Expressing a number as a product of its factors is called factorization. Say, if we write 12=3 x 4 then 12 has been factorized in terms 3 and 4.

Other factorizations of 12 are:

(i)12 = 6x2 =2x3x2

(ii)12 = 4x3 =2x2x3 

In all the above factorizations we always end up with one factorization i.e.

2x2x3 this is called prime factorization.

Conclusively, it can be  stated that, when a natural number is expressed as a product of its prime factors then the factorization of the number is called complete prime factorization.

Other examples of prime factorization:

(i) 24=2x2x2x3

(ii) 9=3x3

(iii) 14=2x7

(iv) 18= 2x3x3 and so on. 

Each of the above is a prime factorization for the given number.