Question

In the following expression, prime factorization has been done?
 $ 54 = 2 \times 3 \times 9 $

Answer 1

Hint: Prime factorization of any number is, writing the number in the multiples of prime factors. Prime number is the number which is not divisible by any number other than one or itself. Check if the numbers that are written in the product are all prime numbers or not.

Complete step-by-step answer:
Prime number is the number which is not divisible by any number other than one or itself. And factorization means a number that divides the given number.
So, prime factorization means the collection of all the numbers which are prime numbers and also, they divide the given number (or you can say, are the factors of the given number). The product of all such numbers in such a way that the product is equal to the given number is called the prime factorization of the given number.
So, by using the concept explained above, we can write the prime factorization of $ 54 $ as
 $ 54 = 2 \times 3 \times 3 \times 3 = 2 \times {3^3} $
Which is clearly, not equal to the RHS of the equation given in the question. In fact, in the RHS of the equation given in the question, $ 54 = 2 \times 3 \times 9 $ , $ 9 $ is not a prime number. But $ 9 $ can be written as $ 3^2 $
So, from the above explanation, we can conclude that, in the expression, $ 54 = 2 \times 3 \times 9 $ , prime factorization has not been done as $ 9 $ is not broken as multiple of 3 $ $

Note: $ 1 $ divides $ 54 $ . But while writing the prime factorization of $ 54 $ , we did not write $ 1 $ because $ 1 $ is not a prime number. $ 1 $ is the exception to the definition of prime numbers. Prime factorization is always the product of primes but the product can never be greater than the given number.