Long Division Calculator

How to Perform Long Division

Long division is a step-by-step method for dividing large numbers. It's a fundamental arithmetic operation that breaks down complex division problems into simpler steps.

Formula

The basic formula for long division is:

\[ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \]

Where:

• Dividend: The number being divided
• Divisor: The number we are dividing by
• Quotient: The result of the division
• Remainder: The amount left over after division

Calculation Steps

1. Write the dividend under the division symbol (√) and the divisor to the left of it.
2. Divide the first digit (or first two digits if necessary) of the dividend by the divisor.
3. Write the result above the division symbol.
4. Multiply this result by the divisor and write the product below the dividend.
5. Subtract this product from the dividend above it.
6. Bring down the next digit from the dividend.
7. Repeat steps 2-6 until there are no more digits to bring down.
8. The final remainder (if any) should be less than the divisor.

Example

Let's divide 725 by 24:

1. Set up the division: 725 ÷ 24
2. 72 is the smallest part of 725 that 24 goes into: \[ \frac{72}{24} = 3 \]
3. Multiply: 24 × 3 = 72
4. Subtract: 72 - 72 = 0
5. Bring down 5: 05
6. Divide again: 5 ÷ 24 = 0 remainder 5

Therefore, 725 ÷ 24 = 30 remainder 5, or 725 = (24 × 30) + 5

Visual Representation

This diagram illustrates the long division process for 725 ÷ 24.