How to Do Long Division, Step by Step
In US schools long division is written with the divisor outside a bracket and the dividend under a bar; each quotient digit goes above the bar, over the last digit it was worked out from. A remainder is usually written with an R, as in 214 R 1.
Every step repeats the same four moves — divide, multiply, subtract, bring down — until no digits are left. The worked example below shows each line exactly as it is written on paper.
When is long division taught?
- Grade 4 (CCSS 4.NBT.B.6): whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
- Grade 5 (CCSS 5.NBT.B.6): up to four-digit dividends and two-digit divisors.
- Grade 6 (CCSS 6.NS.B.2): fluent division of multi-digit numbers using the standard algorithm.
Worked example: 857 ÷ 4
4857
214 R 1485785417161
Left: the problem as a student sees it. Right: the finished working, as it appears in the answer key of our worksheets.
Step by step
- 1Start with the first digit, 8.
- 2Divide: how many times does 4 go into 8? 2 times, so write 2 in the quotient. Multiply: 2 × 4 = 8. Subtract: 8 − 8 = 0.
- 3Bring down the next digit, 5, to make 5.
- 4Divide: how many times does 4 go into 5? 1 time, so write 1 in the quotient. Multiply: 1 × 4 = 4. Subtract: 5 − 4 = 1.
- 5Bring down the next digit, 7, to make 17.
- 6Divide: how many times does 4 go into 17? 4 times, so write 4 in the quotient. Multiply: 4 × 4 = 16. Subtract: 17 − 16 = 1.
- 7The quotient is 214 and the remainder is 1: 214 R 1.
- 8Check: 4 × 214 + 1 = 857.
Common mistakes
- Forgetting a 0 in the quotient: when a brought-down number is smaller than the divisor, write 0 before bringing down the next digit.
- A remainder that is too big: after every subtraction the result must be smaller than the divisor. If it is not, the quotient digit was too small.
- Misaligned digits: write each quotient digit directly above the last digit of the number it came from.
Printable long division practice
- Long division: 3-digit ÷ 1-digit, with remaindersGrade 4 · CCSS 4.NBT.B.6
- Long division: 4-digit ÷ 1-digit, with remaindersGrade 4 · CCSS 4.NBT.B.6
- Long division: 4-digit ÷ 2-digitGrade 5 · CCSS 5.NBT.B.6
- Long division: 5-digit ÷ 2-digitGrade 6 · CCSS 6.NS.B.2