Question

How do you write the $54$ as a product of primes.

Answer 1

In this question, we need to find the prime factors of $54$. Here, we will determine the factors of $54$, then we will determine the prime factors of $54$, using the method of prime factorization.

Complete step-by step solution:
Here, we need to find the prime factors of $54$ using the prime factorization method.
We know that $54$ is a composite number.
Therefore, the possible factors of $54$ are: $\left( {54 \times 1} \right)$, $\left( {27 \times 2} \right)$, $\left( {3 \times 18} \right)$, $\left( {6 \times 9} \right)$.
Prime factorization is a method of finding prime numbers which multiply to make the original number. A prime number is a natural number greater than that is not a product of two smaller natural numbers.
In prime factorization, we start dividing the number by the first prime number $2$ and continue to divide by $2$ until we get a decimal or remainder. Then divide by $3,5,7,...$ etc. until we get the remainder $1$ with the factors as prime numbers. Then write the numbers as a product of prime numbers.
Thus, prime factorization of $54$ is,
$54 = 2 \times 3 \times 3 \times 3$
This can be also written in exponential form as,
$54 = 2 \times {3^3}$

Note: In this question, it is important to note here that a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than and itself. However, the prime factorization is also known as prime decomposition. And, the prime factorization of the prime number is the number itself and $1$. Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers.