1. What is Long Division?

Long division is a standard division algorithm suitable for dividing multi-digit numbers that breaks down a division problem into a series of easier steps. It finds the quotient and remainder when one integer is divided by another.

2. How Does the Calculator Work?

The calculator uses the standard long division algorithm:

Where:

• Dividend — The number being divided
• Divisor — The number dividing the dividend
• Quotient — The result of the division
• Remainder — The amount left over after division

Explanation: The algorithm repeatedly subtracts multiples of the divisor from the dividend to find the quotient and remainder.

3. Importance of Long Division

Details: Long division is fundamental in arithmetic and forms the basis for more advanced mathematical concepts. It's essential for understanding polynomial division in algebra and is widely used in everyday calculations.

4. Using the Calculator

Tips: Enter positive integers for both dividend and divisor. The divisor must be greater than zero. The calculator will display both the quotient and remainder.

5. Frequently Asked Questions (FAQ)

Q1: What if the divisor is zero?
A: Division by zero is undefined. The calculator requires a divisor greater than zero.

Q2: How is this different from regular division?
A: Long division shows the step-by-step process and provides both quotient and remainder, while regular division typically gives only the quotient.

Q3: Can this handle decimal numbers?
A: This calculator works with integers only. For decimal division, you would need a different approach.

Q4: What's the largest number this can handle?
A: The calculator is limited by PHP's integer size, typically up to 2^63-1 on 64-bit systems.

Q5: How is the remainder calculated?
A: The remainder is what's left after subtracting the largest multiple of the divisor from the dividend.