Long Division Calculator
125 divided by 4 is 31 with a remainder of 1, or 31.25 as a decimal. This long division calculator divides one number by another and shows the whole-number quotient, the remainder, and the full decimal answer in one step. Enter the dividend, which is the number being divided, and the divisor, which is the number you divide by, and the tool returns every common form of the answer at once. Long division comes up whenever a division does not split evenly, such as splitting a bill among friends, converting a fraction to a decimal by hand, checking a homework answer, or working out how many full boxes a quantity fills with some left over. This calculator handles all three common ways to express the result: the quotient and remainder pair used in elementary arithmetic, and the decimal answer used everywhere else.
Quick answer
The dividend is the number being divided, and the divisor is the number you divide by.
What this tells you
- •The dividend is the number being divided, and the divisor is the number you divide by.
- •The quotient is the whole-number result, and the remainder is what is left over after the divisor no longer fits evenly.
- •The decimal answer carries the division past the decimal point instead of stopping at the remainder.
- •A remainder of 0 means the divisor goes into the dividend evenly with nothing left over.
- •Multiplying the divisor by the quotient and adding the remainder always returns the original dividend, which is a quick way to check your work.
How to Use
- 1Enter the dividend, the number you want to divide.
- 2Enter the divisor, the number you are dividing by. It cannot be zero.
- 3Click Calculate to get the quotient, the remainder, the decimal result, and a combined quotient-with-remainder summary.
- 4Use the quotient and remainder pair when you need a whole-number answer plus a leftover, such as splitting items into equal groups.
- 5Use the decimal result when you need a precise numeric answer instead of a whole-number-plus-leftover format.
How It Works
Formula
dividend = divisor x quotient + remainderIn long division, the quotient is how many whole times the divisor fits into the dividend, and the remainder is what is left over. Multiplying the divisor by the quotient and adding the remainder returns the dividend, which is the standard way to verify a division by hand. For 125 divided by 4, the divisor fits 31 times (31 x 4 = 124) with 1 left over, so the answer is 31 remainder 1, or 31.25 as a decimal. The decimal form comes from continuing the division past the remainder by treating it as tenths, hundredths, and so on.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Divide 125 by 4
4 goes into 125 a total of 31 times, which is 124, leaving a remainder of 1. As a decimal, 125 divided by 4 is 31.25.
Divide 100 by 7
7 goes into 100 a total of 14 times, which is 98, leaving a remainder of 2. The decimal answer is a repeating pattern that this tool rounds to 14.285714.
Divide 144 by 12 evenly
12 goes into 144 exactly 12 times with nothing left over, so the remainder is 0 and the decimal answer is a whole number.
Divide a smaller number by a larger one
5 does not fit into 3 at all, so the quotient is 0 and the entire dividend becomes the remainder. As a decimal, 3 divided by 5 is 0.6.
Divide a negative dividend
This calculator truncates toward zero rather than rounding down, so -17 divided by 5 gives a quotient of -3 and a remainder of -2, since -3 x 5 + (-2) = -17.
Packing 1,234 candles into cartons of 28
Dana has 1,234 candles to ship and each carton holds 28. The calculator reports the quotient 44, the remainder 2, and the combined form 44 R 2, which reads as 44 full cartons with 2 candles left over. The decimal 44.071429 answers a different question, how many carton loads the candles make, and it does not tell you how many boxes to order. Dana needs 45 cartons if the 2 extras ship, or 44 if they stay behind. Check: 28 x 44 + 2 = 1,234.
Divisibility rules that shortcut long division
Before you divide, these place-value rules tell you whether the remainder will be zero. Each row gives a four-digit number that passes and the calculator's output for 1,234, which fails every rule except the one for 2.
| Divisor | Rule | A number that passes | 1,234 divided by it |
|---|---|---|---|
| 2 | Last digit is 0, 2, 4, 6, or 8 | 1,234 ends in 4 | 617 R 0 |
| 3 | Digits add to a multiple of 3 | 1,236, digits add to 12 | 411 R 1 (digits add to 10) |
| 4 | Last two digits form a multiple of 4 | 1,236, since 36 = 4 x 9 | 308 R 2 (34 is not a multiple of 4) |
| 5 | Last digit is 0 or 5 | 1,235 | 246 R 4 |
| 6 | Passes both the 2 rule and the 3 rule | 1,236, even with digit sum 12 | 205 R 4 (even, but fails the 3 rule) |
| 8 | Last three digits form a multiple of 8 | 1,240, since 240 = 8 x 30 | 154 R 2 (234 = 8 x 29 + 2) |
| 9 | Digits add to a multiple of 9 | 1,233, digits add to 9 | 137 R 1 (digits add to 10) |
| 10 | Last digit is 0 | 1,230 | 123 R 4 |
| 11 | Alternating sum of the digits, from the right, is 0 or a multiple of 11 | 1,232, since 2 - 3 + 2 - 1 = 0 | 112 R 2 (4 - 3 + 2 - 1 = 2) |
| 12 | Passes both the 3 rule and the 4 rule | 1,236, digit sum 12 and last two digits 36 | 102 R 10 (fails the 3 rule) |
Remainders computed with the calculator above, which reports them as quotient R remainder. The rules follow from place value. Every power of 10 is a multiple of 2 and 5, 10 leaves a remainder of 1 when divided by 3 or 9, and 10 is one short of 11, which is why the 11 rule alternates plus and minus. The Common Core State Standards for Mathematics place multi-digit division with remainders in grade 4 (4.NBT.B.6) and fluent division with the standard algorithm in grade 6 (6.NS.B.2).
Why the same division has three different-looking answers
Quotient-and-remainder, quotient-with-a-fraction, and a decimal answer are all correct ways to express the same division, just formatted for different purposes. Elementary arithmetic favors the quotient and remainder because it avoids fractions and decimals entirely, which makes it easier to teach and check by hand.
The decimal form is more useful in everyday math and most calculators, since it gives a single number you can compare, add, or plug into another formula without tracking two separate values. This tool shows all three forms together so you can pick whichever one fits the situation.
The quotient here is the whole-number part of dividend / divisor, truncated toward zero, and the remainder is whatever is left. That matches the behavior of the % operator in JavaScript, where ECMA-262 specifies that the remainder takes the sign of the dividend, so -17 / 5 gives -3 R -2 while 17 / -5 gives -3 R 2. A floor-based convention, used by Python and by most number theory textbooks, reports -17 / 5 as -4 R 3 instead. Both satisfy dividend = divisor x quotient + remainder, so check which convention your class or software expects before comparing answers.
Division by zero shows no result rather than an error value. In IEEE 754 floating point, which ECMA-262 uses for every JavaScript number, 1 / 0 evaluates to Infinity and 0 / 0 to NaN, so the calculator stops before dividing instead of displaying either. The decimal answer is rounded to 6 places, so 100 / 7 shows 14.285714 even though the exact value repeats the block 285714 forever. Exactness has a ceiling as well. JavaScript numbers are IEEE 754 binary64 values, which represent every integer exactly only up to 9,007,199,254,740,991 (Number.MAX_SAFE_INTEGER in ECMA-262). A dividend beyond that limit loses digits before the division starts, so the quotient and remainder can be wrong in their last places.
Common mistakes
- Swapping the dividend and divisor. The dividend is the number being divided, so 125 / 4 is not the same as 4 / 125.
- Forgetting the remainder. When the division is not even, the leftover amount is the remainder, which the decimal answer turns into digits after the point.
- Dividing by zero. Division by zero is undefined, so the divisor must be a nonzero number.
- Assuming the remainder is always positive. With a negative dividend, this calculator truncates toward zero, which can produce a negative remainder alongside a negative quotient.
- Reading a repeating decimal as exact. A result like 14.285714 is a rounded approximation of a repeating decimal, not the exact fraction value.
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