Long division is a step-by-step method for splitting a large number into equal groups. It is useful when division facts alone are not enough, such as dividing 847 by 5. The method keeps the work organized by handling one place value at a time.
It also helps you see whether the answer is exact or has a remainder.
In the example 847 ÷ 5, the dividend is 847 and the divisor is 5. You divide, multiply, subtract, and bring down until every digit has been used. The quotient is 169 with a remainder of 2, written as 847 ÷ 5 = 169 R2.
You can check the answer with multiplication: 5 × 169 + 2 = 847.
Key Facts
- Dividend ÷ divisor = quotient with possible remainder.
- For 847 ÷ 5, the dividend is 847, the divisor is 5, the quotient is 169, and the remainder is 2.
- Long division cycle: divide, multiply, subtract, bring down, repeat.
- Check formula: divisor × quotient + remainder = dividend.
- For the example: 5 × 169 + 2 = 847.
- A valid whole-number remainder must be less than the divisor, so for division by 5 the remainder can only be 0, 1, 2, 3, or 4.
Vocabulary
- Dividend
- The dividend is the number being divided.
- Divisor
- The divisor is the number you divide by.
- Quotient
- The quotient is the main result of a division problem.
- Remainder
- The remainder is the amount left over when the divisor cannot make another full group.
- Bring down
- To bring down means to move the next digit of the dividend into the current division step.
Common Mistakes to Avoid
- Forgetting to bring down the next digit is wrong because long division must use every digit of the dividend in order.
- Writing a remainder that is equal to or greater than the divisor is wrong because another full group could still be made.
- Subtracting incorrectly after multiplying is wrong because each next step depends on the leftover amount from the previous step.
- Checking only with divisor × quotient is wrong when there is a remainder because the correct check is divisor × quotient + remainder.
Practice Questions
- 1 Use long division to solve 736 ÷ 4. Show each subtraction and bring-down step.
- 2 Use long division to solve 952 ÷ 7. Write the answer with a remainder and check it using divisor × quotient + remainder.
- 3 A student says 847 ÷ 5 = 168 R7. Explain why this answer is not written correctly, even before checking the full calculation.