Question

How do write $$54$$ as a product of prime factors?

Answer 1

Hint: We need to know the first ten prime numbers in the natural numbers. This question describes the operation of multiplication/ division. The final answer should involve only prime numbers. The definition of prime numbers is a number that is divided only by $$1$$ and itself, otherwise, it cannot be divided by any numbers.

Complete step by step solution:
In this question, we have to write $$54$$ as a product of prime number factors.First, we should know about prime numbers. The prime numbers are only divided by $$1$$ and itself.Otherwise, it cannot be divided by any numbers. So, the prime numbers are,
$$2,3,5,7,11,13,....$$
To solve the given question we would divide the $$54$$ as follows,

From the given prime numbers we can use $$2$$. So, when $$2$$ is multiplied with $$27$$ it will be$$54$$. As a next step, we didn’t simplify $$2$$. So, we try to simplify $$27$$. $$27$$ can be divided into $$3$$ and $$9$$. So, we get

From the above step we cannot simplify $$3$$, but we can simplify $$9$$. So, $$9$$ can be simplified as $$3\times 3$$. Here $$3$$ is a prime number so we can go to the next step.

So, the final answer is, the product of prime factor for $$54$$ is shown below,
$$54=2\times 3\times 3\times 3$$
(or)
$$54=2\times 3^3$$

Note: In this type of question we would use the operation of addition/ subtraction/ multiplication/ division. We need to know the first ten prime numbers. Note that $$1$$ is not a prime number and $$1$$ is not a non-prime number, it is an exception. All the factors should be a prime number, we don’t use a non-prime number as a factor. Also, we don’t use this $$0$$ as a factor in this type of question.