Write a program that takes a whole number input from a user and determines whether it's prime. If the number is not prime, display its unique prime factors. Remember that a prime number's factors are only 1 and the prime number itself. Every number that is not prime has a unique prime factorization. For example, consider the number 54 The prime factors of 54 are 2,3,3 and \(3 .\) When the values are multiplied together, the result is 54 For the number \(54,\) the prime factors outpur should be 2 and \(3 .\) Use Sets as part of your solution.

Java is a versatile and powerful programming language used for developing a wide range of applications, from mobile apps to large-scale enterprise systems. It's an object-oriented language, which means it allows developers to create modular programs and reusable code. One of the core principles of Java programming is writing code that is not only functional but also clear and maintainable.

When tackling a problem like prime factorization, Java provides a structured approach to break down the problem into manageable steps. Java's extensive set of built-in libraries can help in implementing algorithms efficiently. For example, the Math library can be incredibly handy when working with numbers, especially to calculate the square root of a number as part of a primality check. By focusing on writing clean code, utilizing Java's libraries, and following best practices, students can develop robust and efficient applications that solve complex mathematical problems.

In mathematics, prime numbers are natural numbers greater than 1 that cannot be formed by multiplying two smaller natural numbers. A prime number check involves determining whether a number is prime or not. In Java, this could be efficiently done by looping from 2 to the square root of the number.

This is because a factor of a number is always less than or equal to its square root. If the number can be divided without a remainder by any number within this range, it's not a prime number. It's important for learners to understand that checking up to the square root is a significant optimization compared to checking up to the number itself, as it greatly reduces the number of iterations and thus the computation time required for the check.

A set is a collection of items that are both unordered, and unique, meaning no duplicates are allowed. This data structure is ideal in scenarios where the uniqueness of elements is a key requirement. In Java, the Set interface is implemented by various classes such as HashSet, LinkedHashSet, and TreeSet, each offering different performance characteristics.

When performing prime factorization, a set is used to store the prime factors. Since prime factorization requires finding only the unique factors of a number, the set effectively handles duplicates by preventing their insertion into the collection. Thus, when the prime factors of a number are displayed, what's shown is a collection of unique factors without any repetition. Understanding how to leverage the properties of sets can greatly simplify the task of storing and managing unique items in a program.