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

Last updated date: 13th Jun 2024
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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.