Long division calculator
576 ÷ 24 is 24 with no remainder, reached in two brought-down digits: 24 goes into 57 twice with 9 left, then into 96 four times exactly. The page prints the bracket the way it is written on paper, with each subtraction under the digits it came from, because the layout is the method.
Every bring-down, every product, every remainder — the layout rather than the answer, because the answer is what a phone already gives you and the layout is what the question was about.
Every step checked against the arithmetic in tests · How we check
7,359 ÷ 23
319.956521
319 remainder 22
The working, one bring-down at a time
| Step | Bring down | Goes in | Subtract | Left |
|---|---|---|---|---|
| 1 | 7 | 0 | 0 × 23 = 0 | 7 |
| 2 | 73 | 3 | 3 × 23 = 69 | 4 |
| 3 | 45 | 1 | 1 × 23 = 23 | 22 |
| 4 | 229 | 9 | 9 × 23 = 207 | 22 |
Each row brings down the next digit onto the remainder above it. A zero in the “goes in” column is a real step — it is the one people skip silently and learners lose track on.
Past the decimal point
The same process, bringing down a zero each time instead of a digit.
| .1 | 220 | 9 | 9 × 23 = 207 | 13 |
| .2 | 130 | 5 | 5 × 23 = 115 | 15 |
| .3 | 150 | 6 | 6 × 23 = 138 | 12 |
| .4 | 120 | 5 | 5 × 23 = 115 | 5 |
| .5 | 50 | 2 | 2 × 23 = 46 | 4 |
| .6 | 40 | 1 | 1 × 23 = 23 | 17 |
Why a repeating decimal has to repeat
Dividing by 7 can leave a remainder of 1 through 6 and nothing else. Keep going past the decimal point and you are drawing from that small bag over and over, so a remainder must eventually come up twice — and once it does, everything that followed it the first time follows again in the same order. The repeat is not a coincidence about sevenths; it is forced by there being finitely many remainders.
It also bounds the period: at most n − 1 digits for a divisor of n. One seventh manages the full six. One third repeats after one. And a divisor whose only prime factors are two and five never repeats at all, because those are the factors of ten and the remainder can reach zero.
Questions people actually ask
- What does "bring down" actually mean?
- Take the remainder from the step above, multiply it by ten, and add the next digit of the dividend. That is the number the divisor goes into next. Written on paper it looks like carrying a digit down the page, which is where the phrase comes from — but the arithmetic is a multiplication by ten and an addition, and seeing it that way makes the decimal steps obvious afterwards.
- Why is there a zero at the start of my answer?
- Because the divisor does not fit into the first digit. 7,359 ÷ 23 starts with 23 into 7, which is zero times — a real step that experienced dividers perform silently. The table above prints it, since skipping it is exactly how a digit goes missing from the quotient.
- How do the decimal places work?
- Identically, except that you bring down a zero instead of a digit. Once the dividend runs out, every step multiplies the remainder by ten and continues. That is why a fraction with a denominator made only of twos and fives terminates: the remainder eventually hits zero.
- Why do some decimals repeat?
- Because a remainder comes back. There are only so many possible remainders — fewer than the divisor — so dividing forever must eventually revisit one, and from that point the digits repeat exactly. One seventh has a period of six because the remainders cycle through six values before returning to 1. That is also why the longest possible repeat for a divisor n is n − 1 digits.
- What is the remainder for?
- It is what is left when you stop at whole numbers, and it is often the answer that matters: 7,359 sweets shared between 23 children is 319 each with 22 left in the bag. A decimal answer of 319.956 is correct and useless for that question.