What is the Prime Factorization of 54?

The prime factorization of 54 is the process of breaking down the number 54 into its prime numbers. Prime factorization is important in various fields of mathematics, including number theory and cryptography.

To find the prime factorization of 54, we start by dividing the number by the smallest prime number, which is 2. If 54 is divisible by 2, we continue dividing by 2 until it is no longer divisible. Then, we move to the next smallest prime number and repeat the process.

Let’s break it down step by step:

1. 54 ÷ 2 = 27
2. 27 ÷ 3 = 9
3. 9 ÷ 3 = 3
4. 3 ÷ 3 = 1

So, the prime factors of 54 are 2, 3, 3, and 3. In exponential form, this can be written as 2 × 3³.

Therefore, the prime factorization of 54 is 2 × 3³.