How to use the long division calculator
- Enter the dividend, the number being divided.
- Enter the divisor, the number you are dividing by. Both must be whole numbers, and the divisor can't be 0.
- Read the quotient and remainder at the top, then follow the table. Each row is one round of divide, multiply, subtract and bring down.
- The decimal answer appears underneath. If it repeats, the repeating digits are shown in brackets and with a bar over them.
How long division works
Long division breaks one hard division into many easy ones. Start with the leftmost digits of the dividend that make a number at least as big as the divisor. Divide to find how many times the divisor fits, which gives one digit of the quotient. Multiply that digit by the divisor, subtract it, and bring down the next digit beside what is left. Repeat until no digits remain. What is left at the end is the remainder.
To keep going past the decimal point, add a decimal point to the quotient and bring down zeros. Because every remainder is smaller than the divisor, there are only a limited number of possible remainders. Sooner or later a remainder is 0 and the decimal ends, or one comes back and the digits repeat in a cycle.
Worked example
The calculator opens with 1,234 ÷ 7:
| Step | Working number | Divide | Multiply | Subtract |
|---|---|---|---|---|
| 1 | 12 (1 is too small) | 12 ÷ 7 = 1 | 1 × 7 = 7 | 12 − 7 = 5 |
| 2 | 53 (bring down 3) | 53 ÷ 7 = 7 | 7 × 7 = 49 | 53 − 49 = 4 |
| 3 | 44 (bring down 4) | 44 ÷ 7 = 6 | 6 × 7 = 42 | 44 − 42 = 2 |
Reading down the Divide column gives the quotient 176, and the remainder is 2. So 1,234 ÷ 7 = 176 R 2. Check: 7 × 176 + 2 = 1,232 + 2 = 1,234.
Carrying on past the decimal point, bring down zeros: 20 ÷ 7 = 2 r 6, 60 ÷ 7 = 8 r 4, 40 ÷ 7 = 5 r 5, 50 ÷ 7 = 7 r 1, 10 ÷ 7 = 1 r 3, 30 ÷ 7 = 4 r 2. The remainder 2 has come back, so the digits 285714 repeat forever: 1,234 ÷ 7 = 176.(285714) = 176.285714285714…
Remainder, fraction or decimal?
The same answer can be written three ways, and which one you want depends on the question:
| Form | 1,234 ÷ 7 | When to use it |
|---|---|---|
| Quotient and remainder | 176 R 2 | Sharing whole items: 1,234 stickers among 7 people gives 176 each, with 2 left over |
| Mixed number | 176 2/7 | Exact answers in fraction work |
| Decimal | 176.(285714) ≈ 176.29 | Measurements, money and calculators |
A decimal ends only when the divisor, after canceling common factors with the dividend, has no prime factors other than 2 and 5. Dividing by 8 = 2³ ends (100 ÷ 8 = 12.5), while dividing by 7, 3 or 11 repeats.
Dividing decimals
Long division needs a whole-number divisor, so shift the decimal point first. Multiply the dividend and the divisor by the same power of 10 until both are whole: 7.5 ÷ 0.25 is the same as 750 ÷ 25 = 30. The answer doesn't change, because you scaled both numbers equally. The remainder does scale, though, so read it in the new units.
Frequently asked questions
What does R mean in a division answer?
R stands for remainder, the amount left over when the divisor doesn't fit exactly. 100 ÷ 8 = 12 R 4 means 8 fits into 100 twelve times, using 96, with 4 left. As a fraction that is 12 4/8 = 12 1/2, and as a decimal 12.5.
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 × 7 = 1,232, and 1,232 + 2 = 1,234, so the answer is right.
What do I do when the divisor doesn't fit into the first digit?
Use more digits. In 1,234 ÷ 7, the first digit 1 is smaller than 7, so start with 12. In handwritten work you can write a 0 above the 1 or leave it blank. Either way, the quotient starts in the column of the last digit you used.
How long can the repeating part of a decimal be?
Up to one less than the divisor. Dividing by 7 can repeat every 6 digits at most, and it does: 1/7 = 0.(142857). Dividing by 17 repeats every 16 digits. The calculator checks up to 2,000 decimal digits to find the cycle.
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