Long Division Calculator
Divide whole numbers and see every bring-down, subtract, and remainder step.
Remainder 7 · 4567 ÷ 12 = 380.583333
- Step 1: 12 into 45 goes 3 → 3 × 12 = 36; 45 − 36 = 9
- Step 2: 12 into 96 goes 8 → 8 × 12 = 96; 96 − 96 = 0
- Step 3: 12 into 7 goes 0 → 0 × 12 = 0; 7 − 0 = 7
Reading the quotient digits top to bottom gives 380, and the last remainder is 7.
Long division breaks a big division into digit-by-digit steps. Dividing 4567 by 12 gives a quotient of 380 with a remainder of 7, because 12 × 380 = 4560 and 4560 + 7 = 4567. Each step divides, multiplies, subtracts, then brings down the next digit.
What long division does
Long division splits a hard division into a repeating four-move loop applied to one digit at a time. You work left to right across the dividend, keeping a running remainder, so even large numbers reduce to single-digit multiplication and subtraction. The final answer is a quotient (how many whole times the divisor fits) plus a remainder (what is left over, always smaller than the divisor).
The repeating loop
At every position you divide the current partial number by the divisor, multiply that digit back by the divisor, subtract to find the new remainder, then bring down the next digit and repeat. When there are no digits left to bring down, whatever is left is the remainder.
Worked example — 4567 ÷ 12
Start from the left, taking as many digits as needed until the divisor fits, then carry each remainder forward:
- 1 Find the first group of digits the divisor fits into. 12 does not fit into 4, so take 45. 12 into 45 goes 3 times (3 × 12 = 36); 45 − 36 = 9. First quotient digit: 3.
- 2 Bring down the next digit. Bring down the 6 to make 96. 12 into 96 goes 8 times (8 × 12 = 96); 96 − 96 = 0. Next quotient digit: 8.
- 3 Bring down the next digit. Bring down the 7 to make 7. 12 into 7 goes 0 times (0 × 12 = 0); 7 − 0 = 7. Next quotient digit: 0.
- 4 Read off the answer. No digits remain. Reading the quotient digits gives 380, and the leftover 7 is the remainder — so 4567 ÷ 12 = 380 remainder 7.
The four repeating steps
Apply this loop to each digit position, carrying the remainder forward, until every digit of the dividend is used.
| Step | Action | Example (12 into 45) |
|---|---|---|
| Divide | How many times does the divisor fit the current number? | 45 ÷ 12 → 3 |
| Multiply | Multiply that digit back by the divisor. | 3 × 12 = 36 |
| Subtract | Subtract the product to get the new remainder. | 45 − 36 = 9 |
| Bring down | Drop the next dividend digit beside the remainder. | 9 → 96, then repeat |
Checking your answer
Every long division satisfies quotient × divisor + remainder = dividend. For the example, 380 × 12 + 7 = 4560 + 7 = 4567, which matches — so the answer is correct. If your check does not reproduce the dividend, a subtraction or a quotient digit is off.
The remainder must always be smaller than the divisor. If a remainder ever comes out equal to or larger than the divisor, the quotient digit at that step was too small — the divisor still fits one more time. A remainder of 0 means the division is exact and the divisor is a factor of the dividend.