Q:

What is the prime factorization of 54?

A:

The prime factorization of 54 is 2 x 3 x 3 x 3, which can also be written as 2 x 33. Prime factors are the prime numbers that are multiplied to get another number. A prime number is any number that can only be divided by itself and 1, such as 3, 5 and 17; numbers that can be divided by other numbers are called composite numbers.

The only even number that is a prime number is 2, and 2 is a prime factor of every even number. Therefore, to find the prime factors of 54, the first step is to divide by 2. This results in 27, which cannot be divided by 2. The next step is to determine whether 27 can be further divided. When it is divided by 3, the result is 9. Since 3 is a prime number, it is the second prime factor of 54. The number 9 can be further divided into 3 x 3. The full prime factorization of 54 is 2 x 3 x 3 x 3.

Prime numbers can be considered the building blocks of numbers. Every number has its own unique set of prime factors. This fact is known as the Fundamental Theorem of Arithmetic. Prime factorization is useful in cryptology and computer encryption because it can take a long time for computers to determine the set of prime factors for large numbers.


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