(Odd or Even) Write an application that reads an integer and determines and prints whether it's odd or cven. [Hint: Use the remainder operator. An even number is a multiple of 2. Any multiple of \(2 \text { leaves a remainder of } 0 \text { when divided by } 2 .]\)

In Java programming, the remainder operator, denoted by '%', is a crucial tool for determining certain properties of numbers. It calculates the remainder left over after dividing one number by another. For instance, when you divide 5 by 2 using the remainder operator (5 % 2), the result is 1 because 5 is not completely divisible by 2, thus leaving behind a remainder of 1. This operation is essential in various applications, including determining the parity of an integer - whether it is odd or even.

While the operator is simple, it’s vital to comprehend its function thoroughly. Different than division that gives you the quotient, the remainder operator gives you the leftover part of the equation. Imagine sharing cookies with a friend, if you have 5 cookies and you give 2 to your friend, using the remainder operator basically answers the question, 'How many cookies will I have left after sharing?' In this context, you're left with 1 cookie.

An even number is one that can be divided by 2 with no remainder left. This characteristic of even numbers is pivotal when writing Java programs that need to make decisions based on number parity.

Using the remainder operator effectively allows for even number determination in an application. To put it into code, if you have an integer variable called num, you would write the conditional statement as if (num % 2 == 0). If this condition evaluates to true, it means that there is no remainder and num is an even number. This is how a program can categorize a number as even or not. It’s a straightforward method, yet absolutely fundamental, especially when considering that so many further computations or logical operations in computer science hinge on this bit of knowledge.

On the flip side, determining an odd number involves checking for a remainder of 1 when dividing the number by 2. Odd numbers are an integral aspect to understand, In contrast to even numbers, which form a neat, divisible-by-2 set, odd numbers are those integers that leave a remainder of 1.

For example, in Java, to test if an integer num is odd, you would use the conditional statement if (num % 2 == 1). If the condition is satisfied, num is indeed an odd number. Since odd numbers are not completely divisible by 2, they play a significant role in a wide spectrum of computational cases, such as iterating over, selecting, or grouping elements.