1. What is Divisibility Check?

A divisibility check determines whether one integer can be divided by another integer without leaving a remainder. This is a fundamental concept in number theory and arithmetic.

2. How Does the Calculator Work?

The calculator uses the modulo operation:

Where:

• \( n \) — The number being checked
• \( d \) — The divisor
• \( \mod \) — Modulo operation (remainder after division)

Explanation: If the remainder of n divided by d is zero, then n is divisible by d.

3. Importance of Divisibility

Details: Divisibility checks are essential in many areas including cryptography, computer science algorithms, simplifying fractions, and solving mathematical problems.

4. Using the Calculator

Tips: Enter both numbers as integers. The divisor must be non-zero. The calculator will determine if the first number is divisible by the second.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter zero as the divisor?
A: Division by zero is undefined, so the calculator will show an error message.

Q2: Can I check divisibility for negative numbers?
A: Yes, the calculator works with both positive and negative integers.

Q3: What's the difference between division and divisibility?
A: Division gives a quotient result, while divisibility is a yes/no question about whether division would produce an integer result.

Q4: Are there special rules for divisibility?
A: Yes, there are special rules for certain divisors (like 2, 3, 5, 9, 10) that don't require full division.

Q5: How is this used in programming?
A: Divisibility checks are commonly used in loops, conditional statements, and algorithm design (e.g., FizzBuzz problem).