1. What is Divisibility?

A number N is divisible by another number D if when N is divided by D, the remainder is 0. This is a fundamental concept in number theory and mathematics.

2. How Does the Calculator Work?

The calculator uses the modulo operation:

Where:

• \( N \) — The number being checked
• \( D \) — The divisor
• \( \mod \) — The modulo operation (remainder after division)

Explanation: If the remainder of N divided by D is exactly 0, then N is divisible by D.

3. Importance of Divisibility

Details: Divisibility rules are essential in mathematics for simplifying fractions, factoring numbers, determining prime numbers, and solving various number theory problems.

4. Using the Calculator

Tips: Enter any integer for the number and a non-zero integer for the divisor. The calculator will determine if the number is divisible by the divisor.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I enter zero as the divisor?
A: Division by zero is undefined in mathematics. The calculator will return an error message in this case.

Q2: Does this work for negative numbers?
A: Yes, the calculator works with both positive and negative integers.

Q3: What about decimal numbers?
A: The calculator only works with integers. For decimals, you would need to consider divisibility in the context of real numbers.

Q4: Are there special divisibility rules?
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 different from division?
A: Divisibility checks if division results in an integer, while division gives you the actual quotient which may be fractional.