How long division works
Long division splits one big division into many small ones. Instead of dividing 1,234 by 7 in one go, you divide one digit position at a time, from left to right. Each round has the same four moves, and the calculator labels every one of them in the steps:
- Divide: how many times does the divisor fit into the current number? Write that digit in the quotient.
- Multiply: multiply the divisor by that digit and write the product underneath.
- Subtract: subtract the product. The difference must be smaller than the divisor, or the digit was too small.
- Bring down: bring down the next digit of the dividend next to the difference, and start again.
When there are no digits left to bring down, what is left is the remainder. The names: the dividend is the number you divide, the divisor is the number you divide by, and the quotient is the result.
A worked example: 1,234 ÷ 7
7 does not fit into 1, so start with the first two digits, 12. 7 fits into 12 once: write 1 above the 2, subtract 7 from 12 and get 5. Bring down the 3 to make 53. 7 fits into 53 seven times, since 7 × 7 = 49 and 7 × 8 = 56 is too much. Write 7, subtract 49 and get 4. Bring down the 4 to make 44. 7 fits six times, 6 × 7 = 42, and 44 − 42 = 2. There is nothing left to bring down, so 1,234 ÷ 7 = 176 with a remainder of 2, written 176 R 2.
To check, multiply back: 176 × 7 = 1,232, plus the remainder 2 is 1,234. As a mixed number the answer is 176 2/7, and as a decimal it is about 176.2857.
Finding each digit quickly
The hardest part is guessing how often the divisor fits. With a two-digit divisor like 23, round it to 20 and ask how often 20 fits into the current number. For 70 ÷ 23, 20 fits three times, and 3 × 23 = 69 fits, so the digit is 3. If the product is bigger than the number, try one less. If the difference after subtracting is as large as the divisor or larger, try one more. A quotient digit is always between 0 and 9, and a 0 is a real digit: it must be written, or the other digits shift to the wrong place.
Long division with decimals
A decimal in the dividend is easy: divide as usual and put a decimal point in the quotient straight above the one in the dividend. A decimal in the divisor needs one step first. Move its decimal point to the right until it is a whole number, and move the point in the dividend the same number of places, adding zeros if needed. For 12.345 ÷ 0.5, both numbers are multiplied by 10, which gives 123.45 ÷ 5 = 24.69. Multiplying both numbers by the same amount does not change the answer, just like 12 ÷ 4 and 120 ÷ 40 are both 3.
To keep going past the last digit of the dividend, write a decimal point and add zeros. Each zero you bring down gives one more decimal place in the quotient. The calculator does this when you pick a decimal answer and stops at the number of places you set.
Remainder, fraction or decimal?
The same division can be written in three ways. 1,234 ÷ 7 is 176 R 2 with a remainder, 176 2/7 as a mixed number, and about 176.2857 as a decimal. Which form you want depends on the question. Sharing 1,234 stickers among 7 people, each gets 176 and 2 are left over. For money or measurements you usually want the decimal, rounded to a sensible number of places. The fraction calculator simplifies the fraction form, and the rounding calculator rounds the decimal any way you need.
When the dividend has decimals and you ask for a remainder, the calculator shifts both numbers until they are whole, divides, and then shifts the remainder back. 7.5 ÷ 2 becomes 75 ÷ 20 = 3 R 15, and the 15 is 15 tenths, so 7.5 ÷ 2 = 3 R 1.5. The check works the same: 3 × 2 + 1.5 = 7.5.
Repeating decimals
Some divisions never end. 1 ÷ 3 = 0.333… and 22 ÷ 7 = 3.142857142857…, where the block 142857 repeats forever. You can spot this in the layout: once only zeros are being brought down, each step depends on nothing but the remainder. A remainder is always smaller than the divisor, so sooner or later one comes back, and from then on every step repeats. The calculator watches for that moment and marks the repeating digits with a bar over them, the usual notation. A fraction in lowest terms only has a decimal that ends when its denominator has no prime factors other than 2 and 5, which you can test with the prime factorization calculator.
How to use the long division calculator
- 1Type the dividend and the divisor. Whole numbers, decimals and negative numbers all work, with up to 24 digits each.
- 2Pick an answer with a remainder, or a decimal answer and how many decimal places you want at most.
- 3Read the quotient at the top, follow the written layout and the numbered steps, and copy the result or a link that opens the calculator with your division.
Frequently asked questions
What are the dividend, divisor and quotient?
In 156 ÷ 12 = 13, 156 is the dividend (the number being divided), 12 is the divisor (the number you divide by) and 13 is the quotient (the result). When the division does not come out even, what is left over is the remainder.
How do I divide by a decimal?
Move the decimal point of the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. 12.345 ÷ 0.5 becomes 123.45 ÷ 5. Both numbers were multiplied by 10, so the answer stays the same. Then divide as usual and put the decimal point in the quotient straight above the one in the dividend.
How do I write the remainder as a fraction or decimal?
Put the remainder over the divisor. 1,234 ÷ 7 = 176 R 2, so the answer is 176 2/7. For a decimal, keep dividing instead of stopping: add a decimal point and zeros to the dividend and bring the zeros down one at a time. 2/7 gives 0.285714…, so 1,234 ÷ 7 ≈ 176.2857.
How do I know a decimal repeats?
Watch the remainders once you are bringing down only zeros. A remainder can only be a number from 0 to one less than the divisor. As soon as one comes back, every step after it repeats too, so the digits in between repeat forever. 22 ÷ 7 = 3.142857142857…, written with a bar over 142857.
How do I check a long division answer?
Multiply the quotient by the divisor and add the remainder. You should get the dividend back. For 1,234 ÷ 7 = 176 R 2: 176 × 7 = 1,232, and 1,232 + 2 = 1,234. The calculator shows this check under every remainder answer.
What happens with negative numbers?
Divide without the signs, then set the sign: the quotient is negative when exactly one of the two numbers is negative. −84 ÷ 4 = −21, and −84 ÷ −4 = 21. Dividing by 0 is not possible, because no number times 0 gives anything other than 0.