Long Division Calculator (with Remainders)
Divide whole numbers with the long-division bracket, shown step by step — Divide, Multiply, Subtract, Bring down — with the quotient, remainder, and a check.
What is long division?
Long division breaks a division into a repeating four-step cycle so you can divide numbers of any size using only single-digit division. The number inside the bracket is the dividend, the number outside is the divisor, the answer on top is the quotient, and whatever is left over is the remainder.
The four steps: Divide, Multiply, Subtract, Bring down
- Divide the leftmost chunk of the dividend by the divisor; write the whole-number result on top.
- Multiply that quotient digit by the divisor.
- Subtract the product from the current chunk.
- Bring down the next digit and repeat until no digits remain.
Worked example: 487 ÷ 32
- Round 1 — 48 ÷ 32 = 1. Then 1 × 32 = 32, and 48 − 32 = 16. Bring down 7 to make 167.
- Round 2 — 167 ÷ 32 = 5. Then 5 × 32 = 160, and 167 − 160 = 7. No digits left.
So 487 ÷ 32 = 15 R7. Check: 15 × 32 + 7 = 487.
Dividing evenly: 945 ÷ 15
94 ÷ 15 = 6 (remainder 4), bring down 5 to make 45, then 45 ÷ 15 = 3 with remainder 0. So 945 ÷ 15 = 63 exactly, which means 945 is a multiple of 15.
When the dividend is smaller: 7 ÷ 20
20 does not fit into 7, so the quotient is 0 and the remainder is 7: 7 ÷ 20 = 0 R7.
Common mistakes
- Skipping a 0 in the quotient when a chunk is too small.
- Forgetting to bring down the next digit.
- Letting the remainder grow as large as or larger than the divisor.
The remainder here is the same value the modulo calculator returns, and to continue past the remainder into decimals use long division to decimals.
Frequently asked questions
- What are the four steps of long division?
- Divide, Multiply, Subtract, Bring down (sometimes remembered as DMSB). Divide the current chunk by the divisor to get a quotient digit, multiply that digit by the divisor, subtract to get a remainder, then bring down the next digit and repeat.
- What is a remainder?
- The remainder is what is left over when the dividend does not divide evenly. It is always smaller than the divisor. For 487 divided by 32, the quotient is 15 and the remainder is 7, written as 15 R7.
- How do I check a long-division answer?
- Multiply the quotient by the divisor and add the remainder. If it equals the dividend, the answer is correct. For 487 divided by 32, check that 15 times 32 plus 7 equals 487.
- What does it mean when the remainder is 0?
- A remainder of 0 means the dividend is a multiple of the divisor — it divides evenly. For example 945 divided by 15 is exactly 63, so 945 is divisible by 15.
- What if the dividend is smaller than the divisor?
- The quotient is 0 and the remainder is the dividend itself. The divisor goes into the smaller number zero times, so 7 divided by 20 is 0 R7.
- Why is the quotient written above the dividend?
- Each quotient digit sits above the last digit of the chunk it came from, keeping place values aligned. This is why forgetting a 0 in the middle of a quotient is a common error — the columns stop lining up.
- How does long division relate to remainders and modulo?
- The remainder from long division is exactly the modulo (mod) result, and the quotient plus remainder can also be written as a mixed number. So 487 divided by 32 is 15 remainder 7, which is 15 and 7 over 32 as a mixed number, and 487 mod 32 is 7.