1. What is Divisibility?

A number is divisible by another number if the division results in an integer with no remainder. In mathematics, we say that integer A is divisible by integer B (B ≠ 0) if there exists an integer C such that A = B × C.

2. How Does the Calculator Work?

The calculator uses the modulo operation:

Where:

• \( \mod \) — The modulo operation returns the remainder after division
• Number — The integer being checked for divisibility
• Divisor — The integer to divide by (must be non-zero)

3. Importance of Divisibility

Details: Divisibility rules are fundamental in number theory, cryptography, and computer science. They help simplify fractions, factor numbers, and solve various mathematical 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 first number is divisible by the second.

5. Frequently Asked Questions (FAQ)

Q1: Can the divisor be zero?
A: No, division by zero is undefined in mathematics. The calculator will show an error if you try to use zero as a divisor.

Q2: What about negative numbers?
A: The calculator works with both positive and negative integers. For example, -10 is divisible by 5.

Q3: How is this different from division?
A: Divisibility checks if the division would result in an integer with no remainder, rather than calculating the actual quotient.

Q4: What are some practical applications?
A: Divisibility checks are used in determining leap years, checking credit card numbers (Luhn algorithm), and optimizing computer algorithms.

Q5: Can I check divisibility by decimal numbers?
A: This calculator only works with integers. For decimals, you would need to check if the division results in a finite decimal.