Long division with remainder
784 divided by 12 is 65 with 4 left over. The tool writes the check, 784 = 12 × 65 + 4, and lists every column step, bring down, multiply and subtract, the way it is done on a worksheet. Whole numbers only. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Dividend
- 784
- Divisor
- 12
- Quotient
- 65
- Remainder
- 4
- Notation
- 65 R 4
- Equation
- 784 = 12 × 65 + 4
Long division is the first algorithm most children meet that returns two answers at once: a whole-number quotient and a remainder strictly smaller than the divisor. This calculator divides one whole number by another, writes the identity dividend equals divisor times quotient plus remainder, and lists the classroom steps that produce those two integers. Teachers use it to check homework; parents use it when the textbook page is already closed; exam writers use it as a deterministic oracle that never rounds a leftover into a decimal. Failed input is not billed.
What long division with remainder means
Whole-number division asks a concrete classroom question: how many complete groups of the divisor fit inside the dividend, and how many units are left over? The pair of answers is the quotient and the remainder. Together they satisfy the division algorithm that every elementary program eventually writes on the board: the dividend equals the divisor times the quotient plus the remainder, and the remainder is a whole number strictly smaller than the divisor.
When the remainder is zero the division is exact and the dividend is a multiple of the divisor. When the remainder is positive the leftover is real, not a rounding error, and must be reported as a remainder rather than smuggled into a repeating decimal. Long division is the digit-by-digit procedure that finds that pair without a calculator memory: bring down the next digit of the dividend, ask how many times the divisor fits into the working number, multiply, subtract, and carry the new remainder to the next column.
The contract is two whole numbers in and a checked identity out, plus the list of column steps a teacher would tick on a worksheet. That is the foundation of long division as it is taught in elementary school, not a computer-algebra rewrite of a polynomial ring.
What you enter and what each step shows
A divisor of zero is rejected as division by zero. Both values must sit between the published bounds, from zero through one trillion for the dividend and from one through one trillion for the divisor, so every intermediate product stays inside safe integer arithmetic. Each step records index, the digit brought down, the working partial, how many times the divisor fits (times), the product, and the column remainder after subtraction.
Leading zero quotient digits are omitted until the first non-zero digit, except when the whole dividend is smaller than the divisor, in which case the quotient is zero, the remainder is the dividend, and a single step records that fact. Example: dividend seven hundred eighty-four and divisor twelve yields quotient sixty-five, remainder four, notation sixty-five R four, and the equation seven hundred eighty-four equals twelve times sixty-five plus four. Those validation failures are not billed.
Who uses it to check long division
Classrooms and tutoring platforms use a long division with remainder calculator so learners can check both the quotient and the leftover for arbitrary whole numbers without dropping a digit in the subtract step. Homework generators and learning-management graders need a deterministic oracle that marks a decimal-only answer wrong when the item asked for remainder form, and that never invents a remainder greater than or equal to the divisor.
Parents checking a fourth-grade packet want the same identity the teacher will mark: dividend equals divisor times quotient plus remainder, written in classroom language rather than as a floating-point quotient. Failed validation does not consume balance. Keep requests inside the published whole-number limits, pin quotient, remainder, and the equation in tests, and you get reproducible remainders for worksheets, LMS plugins, and edge workers without standing up a computer-algebra system for a two-integer problem.
When the search is polynomial long division or synthetic division by a linear factor, use those dedicated landings; this page stays on the elementary whole-number algorithm.
What you can do with it
Classroom and homework checks
Let students submit a dividend and a divisor and verify the quotient, remainder, and division-algorithm identity against the long-division steps they wrote by hand.
Exam and LMS auto-grading
Mark remainder-form items with a deterministic oracle that never accepts a leftover greater than or equal to the divisor and never silently returns a decimal.
Worksheet and packet generators
Build printable long-division practice with known answers: pin quotient, remainder, and the equation so every generated item has a unique checked key.
FAQ
How do I divide two whole numbers and get a remainder?
Send whole numbers dividend (zero or more) and divisor (at least one).
When is the remainder zero?
When the dividend is an exact multiple of the divisor. In that case exact is true and notation is just the quotient, with no R leftover.
Does this solve polynomial long division?
No. This landing divides two whole numbers the way elementary school teaches long division. Polynomial long division is a different search and a different capability.
What does 65 R 4 mean in long division?
It means a quotient of 65 and a remainder of 4. You can check it by multiplying the divisor by the quotient and adding the remainder: 12 × 65 + 4 gives back 784, the number you started with.
Why do I get a remainder instead of a decimal?
Because whole-number division answers how many complete groups fit and how many units are left. The leftover is reported as it is, never rounded into a decimal; if you need a mixed number, build it from the remainder and the divisor.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/edu/long-division-steps \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"dividend":784,"divisor":12}'const res = await fetch("https://api.kit.forhosting.com/edu/long-division-steps", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"dividend": 784,
"divisor": 12
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/edu/long-division-steps",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"dividend": 784,
"divisor": 12
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/edu/long-division-steps", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"dividend":784,"divisor":12}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"dividend":784,"divisor":12}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/edu/long-division-steps", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"dividend": 784,
"divisor": 12
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "edu.long_division_steps",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_value | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
The same pure module powers the free browser tool and the API, so a printed worksheet and an automated grader never disagree on seven hundred eighty-four divided by twelve. Every successful API call costs $0.002.
What long division with remainder means
This endpoint runs that same procedure. It does not convert the leftover into a mixed number unless you do that yourself from the two integers, and it does not perform polynomial long division, which is a different search with a different landing.
Input contract, steps payload, and error behaviour
POST a JSON body with two required whole numbers: dividend, the non-negative integer being divided, and divisor, the positive integer you divide by. Each field may arrive as a JSON integer or as a digit string; empty strings, decimals, infinities, and missing fields fail with invalid_input naming the field. On success the body echoes dividend and divisor, then returns quotient, remainder, exact (true when the remainder is zero), notation such as sixty-five R four, the equation that restates the division algorithm, the formula string, step_count, and steps. Pair the integers with your own worksheet layout if you need the traditional house-shaped tableau; this endpoint solves the arithmetic and lists the columns, it does not emit a drawing.
Technical questions
What happens if the divisor is zero?
The task fails with invalid_input. Division by zero is undefined, so the request is rejected and is not billed.
What does the long division calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.