Question

Write an application that reads two integers, determines whether the first is a multiple of the second and prints the result. [Hint: Use the remainder operator.]

Short answer

Use the remainder operator to determine if the first integer is a multiple of the second and print the result.

Step-by-step solution

Request Input

Prompt the user to input two integers. This can be achieved in most programming languages using a function like `input()` in Python, `Scanner` in Java, or `cin` in C++.

Read the Integers

Read the user input and store the values in two separate variables. Ensure that the inputs are correctly converted to integers.

Use the Remainder Operator

Use the remainder operator (commonly denoted as `%` in many programming languages) to calculate the remainder of the division of the first integer by the second integer.

Determine Multiplicity

Check if the remainder from Step 3 is zero. If so, the first integer is a multiple of the second. Otherwise, it is not.

Print the Result

Print the result to the user. If the first integer is a multiple of the second, print a message indicating this. If not, print a message saying the first integer is not a multiple of the second.

Key concepts

Remainder Operator

Understanding the remainder operator, typically symbolized as \(\%\), is essential for various computations in programming. It performs what's known as modulus division, returning the remainder after division of two numbers. For example, the expression \(5 \% 2\) equals \(1\), as 2 goes into 5 twice, with 1 left over.

In our exercise, when we consider whether one number is a multiple of another, the remainder operator is our go-to tool. If you divide a number by one of its multiples, the remainder will always be zero since it fits perfectly, like \(6 \% 3\) which equals \(0\), confirming that 6 is indeed a multiple of 3.

Conditional Statements

Conditional statements, such as \(if\), \(else if\), and \(else\), are the decision-making backbones of programming. They assess a condition and direct the flow of the program accordingly. If the condition is true, a set of instructions is executed; if not, the program moves on to evaluate the next condition or closes the conditional block.

In the context of our exercise, a conditional statement is used to compare the result of the remainder operation to zero. You could write the statement as follows: \(if (firstInteger \% secondInteger == 0)\), then you know the first integer is a multiple of the second and you can instruct the program to print the corresponding message.

Input and Output

Input and output operations are critical for interacting with users. Input allows a program to gather data from the user, while output enables the program to communicate results back to them.

For our exercise, the input mechanism could be a simple prompt requesting the user to enter two integers. This might look like \(Enter the first integer: \) and \(Enter the second integer: \) in the command line. After processing the user's input through the steps involving the remainder operator and the conditional statement, the program provides output by printing the result, be it a confirmation of multiplicity or a statement of its absence.