1. What is Divisibility?

Divisibility in mathematics means that one integer can be divided by another integer without leaving any remainder. If a % b == 0, we say "a is divisible by b" or "b divides a".

2. How Does the Calculator Work?

The calculator uses the modulo operation:

Where:

• \( a \) — The number being divided (dividend)
• \( b \) — The divisor
• \( \% \) — The modulo operator that returns the remainder

Explanation: If the remainder of a divided by b is zero, then a is divisible by b.

3. Importance of Divisibility

Details: Divisibility rules are fundamental in number theory, cryptography, computer science algorithms, and simplifying fractions in arithmetic.

4. Using the Calculator

Tips: Enter two positive integers. The second number (b) must be greater than 0. The calculator will determine if the first number is divisible by the second.

5. Frequently Asked Questions (FAQ)

Q1: What happens if b is zero?
A: Division by zero is undefined in mathematics, so the calculator will return "Undefined".

Q2: Can I check divisibility for decimal numbers?
A: This calculator works with integers only. For decimals, the concept of divisibility is different.

Q3: What are some common divisibility rules?
A: For example: A number is divisible by 2 if it's even, by 3 if the sum of its digits is divisible by 3, etc.

Q4: How is this different from division?
A: Division gives a quotient, while divisibility checks if the division would result in an integer with no remainder.

Q5: Where is divisibility used in real life?
A: In scheduling, cryptography, error detection codes, and when working with periodic patterns.