(Check a number) Write a program that prompts the user to...

(Check a number) Write a program that prompts the user to enter an integer and checks whether the number is divisible by both 5 and $6,$ divisible by 5 or $6,$ or just one of them (but not both). Here is a sample run:

Key Concepts

Modular Arithmetic

Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after reaching a certain value—the modulus. In programming, the modulus operator (%) is used to compute the remainder after division, which is especially useful for checking divisibility; if the remainder is zero, then the number is divisible by the divisor.

Divisibility

Divisibility refers to the ability of one integer to be divided by another without leaving a remainder. This concept is crucial in many programming problems, enabling the determination of whether a given number meets specific criteria, such as being divisible by several numbers simultaneously or exclusively.

Conditional Statements

Conditional statements, such as if, else if, and else, enable a program to execute certain sections of code based on whether specific conditions are met. They are fundamental in decision-making processes in programming, where multiple outcomes can be handled depending on the result of a logical test.

Logical Operators

Logical operators, including AND, OR, and NOT, are used to combine or invert boolean expressions. They allow for complex condition evaluations, such as checking if a number meets multiple divisibility criteria or only one of several conditions, thereby directing the flow of the program based on combined logical conditions.

User Input Handling

User input handling involves techniques to receive and process data provided by the user, which is essential for interactive programs. It ensures that the program can accept an integer from the user, validate it, and then proceed with further operations based on that input, such as checking for divisibility.

Transcript

00:01 Hello, for problem 12 in chapter 4, you're asked to write a program that will prompt the user to enter an integer and then to check whether or not that integer is divisible by 5, 6 or both.

00:15 So we'll start by receiving the integer by denoting that integer as number and evaluating the input by the user, where we prompt the user by printing and enter an integer.

00:30 Then we need to check if it's divisible by five or six.

00:33 So div by five is going to be number, the modulo five is equal to zero.

00:39 If that's true, then div by five will be true.

00:42 If that's false, div by five will be false.

00:45 And same for six.

00:47 And then to display the results, we want to print out the questions, is number divisible by five and six? is number divisible by five or six? and is number divisible by five or six, but not both? and after each of those questions, we're going to print out for divisible by five and a six, we need div by five and div by six to be true.

01:10 For divisible by five or six, we need div by five or div by six to be true.

01:15 And if divisible by five or six, but not both, we need div by five or div by six to be true and not div by five and div by six to be true.

01:28 So let's go ahead and try some numbers.

01:32 We'll first start by a number that is divisible by five but not six.

01:36 So we see 15 is divisible by five and six...

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