Long Division Calculator with Steps
Divide any two whole numbers and see every step of the classic long-division method: quotient, remainder, the subtraction at each digit, and the decimal expansion with repeating decimals detected automatically.
Calculator
Step-by-step: integer part
| Bring down | Divide | Multiply | Subtract |
|---|
Step-by-step: decimal part
| Remainder × 10 | Divide | Multiply | Subtract |
|---|
Worked examples
Each example below was computed and verified by an independent exact-arithmetic oracle before publication.
100 ÷ 7
Quotient 14 · Remainder 2
Decimal: 14.285714…
Check: 14 × 7 + 2 = 100
| Divide | Multiply | Subtract |
|---|---|---|
| bring down 1 → 1 | too small — no digit yet | |
| 10 ÷ 7 = 1 | 1 × 7 = 7 | 10 − 7 = 3 |
| 30 ÷ 7 = 4 | 4 × 7 = 28 | 30 − 28 = 2 |
1 ÷ 3
Quotient 0 · Remainder 1
Decimal: 0.3…
Check: 0 × 3 + 1 = 1
| Divide | Multiply | Subtract |
|---|---|---|
| 1 ÷ 3 = 0 | 0 × 3 = 0 | 1 − 0 = 1 |
144 ÷ 12
Quotient 12 · Remainder 0
Decimal: 12 (exact)
Check: 12 × 12 + 0 = 144
| Divide | Multiply | Subtract |
|---|---|---|
| bring down 1 → 1 | too small — no digit yet | |
| 14 ÷ 12 = 1 | 1 × 12 = 12 | 14 − 12 = 2 |
| 24 ÷ 12 = 2 | 2 × 12 = 24 | 24 − 24 = 0 |
22 ÷ 7
Quotient 3 · Remainder 1
Decimal: 3.142857…
Check: 3 × 7 + 1 = 22
| Divide | Multiply | Subtract |
|---|---|---|
| bring down 2 → 2 | too small — no digit yet | |
| 22 ÷ 7 = 3 | 3 × 7 = 21 | 22 − 21 = 1 |
How long division works
Long division breaks a division into a repeating four-move cycle applied to one digit at a time:
- Divide — how many times does the divisor fit into the current partial number?
- Multiply — multiply that digit by the divisor.
- Subtract — subtract the product from the partial number.
- Bring down — bring down the next digit and repeat.
When the digits run out, the leftover is the remainder. Continuing past the decimal point (bringing down zeros) produces the decimal expansion. If a remainder ever repeats, the digits from that point repeat forever — a repeating decimal, shown above with an overline, e.g. 14.285714. If the remainder reaches zero, the decimal terminates.
Frequently asked questions
What is long division?
Long division is a step-by-step method for dividing one whole number by another. You work through the digits of the dividend one at a time, repeatedly dividing, multiplying, subtracting, and bringing down the next digit, until you get a quotient and a remainder.
How do you do long division step by step?
Take the leftmost digits of the dividend that are at least as big as the divisor, then repeat four moves: divide to get the next quotient digit, multiply it by the divisor, subtract the product, and bring down the next digit. When no digits remain, the leftover is the remainder.
What is 100 divided by 7?
100 divided by 7 is 14 with a remainder of 2. As a decimal it is 14.285714285714 and so on, with the six digits 285714 repeating forever. You can check it: 14 times 7 plus 2 equals 100.
Why does 1 divided by 3 never end?
Because the remainder never reaches zero. Dividing 1 by 3, every step leaves remainder 1, so the digit 3 repeats forever: 0.333 and so on. Any division whose remainder repeats produces a repeating decimal instead of terminating.
What is a repeating decimal?
A repeating decimal is a decimal whose digits eventually repeat the same block forever, like 0.1666 and so on or 3.142857142857 and so on. It happens exactly when a remainder repeats during long division. This calculator marks the repeating block with an overline.
What is the difference between the quotient and the remainder?
The quotient is the whole-number result of the division, and the remainder is what is left over. For 100 divided by 7, the quotient is 14 and the remainder is 2, because 7 fits into 100 fourteen times with 2 left over.
Can the divisor be bigger than the dividend?
Yes. If the divisor is bigger, the quotient is 0 and the remainder equals the dividend. For example, 3 divided by 7 is 0 with remainder 3, and the decimal expansion is 0.428571428571 and so on.
How do I check my long division answer?
Multiply the quotient by the divisor and add the remainder. The result must equal the dividend. For example, 14 times 7 plus 2 equals 100, which confirms that 100 divided by 7 is 14 remainder 2. This calculator shows the check automatically.
What does it mean when the decimal terminates?
It means the remainder reached zero, so no more digits are needed. For example, 144 divided by 12 is exactly 12, and 5 divided by 2 is exactly 2.5. After removing common factors with the dividend, this happens exactly when the divisor's only prime factors are 2 and 5.
How many decimal digits does this calculator show?
Up to 120 decimal digits. If a repeating cycle is found within those digits, the repeating block is marked with an overline. If the cycle is longer than 120 digits, the expansion is truncated and labeled, which is rare and only happens with large prime divisors.
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