Table of Contents
- What Is Long Division?
- How to Use the Long Division Calculator
- Worked Example: 945 ÷ 7 Step by Step
- Long Division with Remainders
- More Long Division Examples
- How to Check Your Answer
- Common Mistakes to Avoid
- FAQs
Long division is the written method for dividing bigger numbers, built from one repeating pattern: divide, multiply, subtract, bring down. It looks long on paper, but each step is small, and once the pattern clicks it works for numbers of any size. Use this long division calculator with steps at the top of this page to divide any two whole numbers and see every step written out in words, then read on for a full walkthrough of 945 ÷ 7, how remainders work, and how to check any long division answer in seconds.
Long Division Calculator with Steps
| Quotient (whole number) | |
| Remainder | |
| Decimal answer (2 decimal places) | |
| Decimal answer (4 decimal places) |
Whole numbers only. The steps follow the standard long division method taught in school.
What Is Long Division?
Division splits a number into equal groups. The number being split is the dividend, the number you split by is the divisor, and the answer is the quotient. When the split is not exact, a remainder is left over. Long division handles the split digit by digit, starting from the left of the dividend, instead of trying to swallow the whole number at once.
The method matters because it always works with nothing more than your times tables. Short division is its quicker cousin, used when the divisor is small and the steps can be held in your head, but long division writes everything down — which is exactly why it is the version taught for two-digit divisors and large dividends, and why seeing the steps laid out makes homework and exam questions much easier to follow. The same patient, one-digit-at-a-time approach runs through the Khan Academy arithmetic course, whose multi-digit division lessons follow this method.
Two terms are worth fixing before we start. The partial dividend is the small number you are working on at each step — the first chunk of the dividend big enough to divide. And each step ends by bringing down the next digit of the dividend, which grows the partial dividend for the step that follows.
How to Use the Long Division Calculator
Enter the dividend in the first box and the divisor in the second, then press Divide with Steps — that is all the long division calculator with steps needs to start. The tool shows the quotient, the remainder, and the answer as a decimal to two and four decimal places. Underneath, it lists the steps in plain sentences: how many times the divisor goes into each partial dividend, the multiplication, the subtraction, and which digit is brought down next.
The calculator works with whole numbers. If you type a decimal point, a divisor of zero, or a negative number, it explains the problem instead of guessing, because long division in this standard form is a whole-number method. Very large numbers are welcome up to a dividend of 999,999,999 — the step list simply grows longer.
Try following one calculation on paper at the same time as the tool. Matching your written steps against the generated ones is the fastest way to find where a hand-worked answer went wrong.
Worked Example: 945 ÷ 7 Step by Step
Nine hundred and forty-five divided by seven is a tidy first example, because it uses all parts of the method and comes out exact.
Step 1. Look at the first digit of the dividend, 9. How many times does 7 go into 9? Once: 1 × 7 = 7. Subtract: 9 − 7 = 2. Write 1 as the first digit of the quotient. Bring down the next digit, 4, to make 24.
Step 2. How many times does 7 go into 24? Three times: 3 × 7 = 21. Subtract: 24 − 21 = 3. Write 3 in the quotient, next to the 1. Bring down the next digit, 5, to make 35.
Step 3. How many times does 7 go into 35? Five times exactly: 5 × 7 = 35. Subtract: 35 − 35 = 0. Write 5 in the quotient. There are no more digits to bring down and nothing is left over.
The quotient is 135 and the remainder is 0, so 945 ÷ 7 = 135 exactly.
| Step | Partial dividend | Divisor goes in | Multiply | Subtract | Bring down |
|---|---|---|---|---|---|
| 1 | 9 | 1 time | 1 × 7 = 7 | 9 − 7 = 2 | 4, making 24 |
| 2 | 24 | 3 times | 3 × 7 = 21 | 24 − 21 = 3 | 5, making 35 |
| 3 | 35 | 5 times | 5 × 7 = 35 | 35 − 35 = 0 | Nothing left |
Notice the rhythm in this long division calculator with steps: each answer digit comes from the partial dividend, and each subtraction must give a number smaller than the divisor. If a subtraction ever leaves 7 or more here, the quotient digit was too small — that one check catches most errors before they spread.
Long Division with Remainders
Not every division lands exactly. Take 100 ÷ 6. Six goes into 10 once (1 × 6 = 6, remainder 4), then bringing down the 0 gives 40, and six goes into 40 six times (6 × 6 = 36, remainder 4). The digits run out with 4 still left over, so 100 ÷ 6 = 16 remainder 4.
A remainder can be written three ways, and the right choice depends on the question. As a remainder: 16 r4, which suits sharing problems where the leftovers stay whole. As a fraction: 16 and 4/6, which tidies to 16⅔ — our fraction calculator can help with that simplifying step. Or as a decimal: keep dividing by bringing down zeros after a decimal point, giving 16.6667, which rounds to 16.67. The calculator shows the whole-number quotient, the remainder and the decimal side by side so you can pick the form your question wants. Khan Academy’s long division with remainder example walks through the same remainder handling on video.
More Long Division Examples
The two examples below show the method stretching in opposite directions: a two-digit divisor, and a quotient with a zero in the middle, which is the case students most often miss.
Dividing 1234 by 12: twelve does not go into 1, so start with 12 — it goes in once (1 × 12 = 12, remainder 0). Bring down the 3 to make 3; twelve goes into 3 zero times, so a 0 goes in the quotient (0 × 12 = 0, remainder 3). Bring down the 4 to make 34; twelve goes in twice (2 × 12 = 24, remainder 10). The answer is 102 remainder 10, or 102.83 as a decimal. That middle zero is essential: without it the answer would read as 12, not 102.
Dividing 756 by 4 is friendlier: 4 into 7 goes 1 (remainder 3), 4 into 35 goes 8 (8 × 4 = 32, remainder 3), and 4 into 36 goes 9 exactly. The answer is 189 with no remainder.
| Division | Quotient | Remainder | Decimal (2dp) |
|---|---|---|---|
| 945 ÷ 7 | 135 | 0 | 135.00 |
| 100 ÷ 6 | 16 | 4 | 16.67 |
| 1234 ÷ 12 | 102 | 10 | 102.83 |
| 756 ÷ 4 | 189 | 0 | 189.00 |
How to Check Your Answer
Every long division can be checked with one line: divisor × quotient + remainder = dividend. For the remainder example: 6 × 16 + 4 = 96 + 4 = 100, which matches the dividend, so the answer is right. For 1234 ÷ 12: 12 × 102 + 10 = 1224 + 10 = 1234. Correct again.
This check is worth building into a habit, because it uses different operations from the division itself and so catches slips that re-reading your steps would miss. It is the same reverse-check idea used all over maths — the reason our guide on how to calculate a percentage suggests running the numbers backwards, and the reason the average in our average calculator can be checked by multiplying it back by the count. If the check fails, compare your steps against the calculator’s step list to find the first line where they disagree; the mistake is almost always in that step’s multiplication or subtraction.
Common Mistakes to Avoid
Forgetting the zero in the quotient is the most common error, as the 1234 ÷ 12 example showed: when the divisor does not go into the partial dividend, a 0 must still be written before moving on. Skipping it shifts every later digit one place to the left and wrecks the answer.
The second classic slip is a subtraction that leaves a remainder bigger than the divisor — a sure sign the quotient digit was too small — or subtracting wrongly under time pressure. Third, place value: the quotient digits must sit above the correct dividend digits, which is why squared or neatly lined paper genuinely helps. Finally, with remainders, read the question again before choosing the answer form: “how many full boxes” wants the quotient only, “how much is left” wants the remainder, and a measurement usually wants the decimal.
FAQs
What are the steps of long division?
The long division calculator with steps follows a pattern that repeats four moves: divide the partial dividend by the divisor to get the next quotient digit, multiply that digit by the divisor, subtract to find what is left, and bring down the next digit of the dividend. Repeat until no digits remain; whatever is left at the end is the remainder.
What is 945 divided by 7?
945 ÷ 7 = 135 exactly, with no remainder. The steps are: 7 into 9 goes 1 (remainder 2), bring down 4; 7 into 24 goes 3 (remainder 3), bring down 5; 7 into 35 goes 5 exactly.
What do you do with a remainder?
It depends on the question. In this long division calculator with steps, you can leave it as a remainder (16 r4), write it as a fraction over the divisor (16⅔ for 100 ÷ 6, after simplifying 4/6), or keep dividing past a decimal point to get a decimal answer (16.67). Money and measurement questions usually want the decimal; sharing whole objects usually wants the remainder.
How do you check a long division answer?
Multiply the divisor by the quotient and add the remainder. The result must equal the dividend. For example, 6 × 16 + 4 = 100 confirms that 100 ÷ 6 = 16 remainder 4.
What if the divisor is bigger than the dividend?
With whole numbers, the quotient is 0 and the remainder is the whole dividend — 5 ÷ 9 = 0 remainder 5 — because the divisor does not go in even once. As a decimal the answer is a fraction less than 1 (5 ÷ 9 ≈ 0.56), found by adding a decimal point and bringing down zeros.
What is the difference between long division and short division?
Short division does the same maths but keeps the working in your head, writing only small remainders beside each digit. It suits one-digit divisors and confident calculators. Long division writes every multiplication and subtraction in full, which makes it slower but far easier to follow and to check, especially with two-digit divisors.
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