Long Division Calculator

How to use the long division calculator

1. Choose the form of the answer. “Remainder” stops at the ones place and gives a quotient and remainder, the way whole-number division is first taught. “Decimal” keeps going past the decimal point.
2. Enter the dividend and divisor. The dividend is the number being divided; the divisor is the number you divide by. Commas are fine, and either number can be a decimal.
3. Follow the layout and the steps. The layout shows the quotient above the dividend and each product and difference below it. The numbered list spells out every step in words and numbers, so you can compare it line by line with your own work.

The calculator opens on Example 1.64 from OpenStax’s Prealgebra 2e: 1,439 ÷ 4 = 359 R3. Check by multiplying: 359 × 4 + 3 = 1,439.

Divide, multiply, subtract, bring down

Long division repeats four steps until no digits are left to bring down. Here they are for Example 1.61, 2,596 ÷ 4:

1. Divide. 4 doesn’t go into 2, so use the first two digits: 4 goes into 25 six times. Write 6 in the quotient above the 5.
2. Multiply. 6 × 4 = 24. Write it under 25.
3. Subtract. 25 − 24 = 1.
4. Bring down the next digit, 9, to make 19.

Repeat: 4 goes into 19 four times (16, leaving 3); bring down the 6 to make 36; 4 goes into 36 nine times exactly. The quotient is 649 with no remainder.

Each digit of the quotient goes directly above the last digit of the number it came from, which keeps the place values lined up. The layout in the calculator does the same.

Remainders and checking

When the final subtraction doesn’t reach zero, what’s left is the remainder, written with R. It must be smaller than the divisor; if it isn’t, the last quotient digit was too small.

The textbook checks every division by multiplying back: quotient × divisor + remainder should equal the dividend. The “Check” card does this. For 74,521 ÷ 241 (Example 1.66), the answer is 309 R52, and 309 × 241 + 52 = 74,521.

That example also shows a zero in the quotient. After 241 goes into 745 three times (723, leaving 22), bringing down the 2 makes 222, which is smaller than 241. The quotient digit there is 0, and you bring down the next digit to make 2,221. Forgetting the 0 is one of the most common long-division slips.

A remainder can also be written as a fraction of the divisor, giving a mixed number: 1,439 ÷ 4 = 359 3/4.

Choosing each digit with a larger divisor

With a two- or three-digit divisor, the hard part is estimating how many times it fits. The textbook’s advice is to guess and check: round the divisor, estimate, multiply, and adjust if the product is too big or the difference is larger than the divisor. For 1,461 ÷ 13, 13 goes into 14 once, into 16 once, and into 31 twice (26, leaving 5), so the answer is 112 R5. The calculator’s step list shows the exact product at each stage, which makes it easy to see where a hand calculation went off.

Decimal answers

In “Decimal” mode, the division continues past the ones place. Put a decimal point in the quotient directly above the decimal point in the dividend, write zeros after the dividend as needed, and keep bringing them down. 1,439 ÷ 4 continues: the remainder 3 becomes 30, 4 goes into 30 seven times with 2 left, 20 gives 5 with nothing left, so 1,439 ÷ 4 = 359.75.

Some divisions don’t end. When a remainder repeats, the digits after it repeat too. 5 ÷ 7 produces the remainders 5, 1, 3, 2, 6, 4 and then 5 again, so the decimal is 0.714285714285…, written 0.(714285) here, or with a bar over the repeating block. The calculator stops as soon as a remainder repeats and puts the repeating digits in parentheses. Otherwise it stops after 12 decimal places.

Dividing by a decimal

Section 5.2 of the textbook explains how to divide by a decimal: move the decimal point in the divisor all the way to the right to make it a whole number, then move the decimal point in the dividend the same number of places, writing zeros as needed. This multiplies both numbers by the same power of 10, so the quotient doesn’t change.

In Example 5.22, −25.65 ÷ (−0.06): move both points two places to get 2,565 ÷ 6 = 427.5, and the quotient is positive because the signs are the same. In Example 5.21, −2.89 ÷ 3.4 becomes 28.9 ÷ 34 = 0.85, and the different signs make it −0.85. The “Shifted problem” card shows the rewritten division.

The vocabulary of division

In 1,439 ÷ 4 = 359 R3, 1,439 is the dividend, 4 is the divisor, 359 is the quotient and 3 is the remainder. The same problem can be written with a fraction bar, 1,439/4, or with the long-division bracket, where the divisor sits to the left and the dividend under the bar.

Two special cases come straight from the textbook. Zero divided by any nonzero number is 0, since 0 × 3 = 0. But division by zero is undefined: no number times 0 gives 10, so 10 ÷ 0 has no answer, and the calculator reports an error instead of a result.

Division in word problems

The remainder often decides the answer in a real problem. In the textbook’s Example 1.68, 160 ounces of oatmeal split into 8-ounce servings gives 160 ÷ 8 = 20 servings, with nothing left over. But if 50 people need rides in cars that seat 4, 50 ÷ 4 = 12 R2, and you need 13 cars, since the last 2 people still need a seat. If a ribbon of 50 inches is cut into 4-inch pieces, you get 12 pieces and 2 inches of scrap. Same division, three different readings of the remainder: exact, round up, or drop it.

When the answer is money or a measurement, the decimal form is usually what you want: $50 split 4 ways is $12.50 each. Round a long decimal only at the end, and to the precision the problem needs, such as the nearest cent.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Each step: divide, multiply, subtract, bring down the next digit.
• A decimal divisor is made whole by moving both decimal points the same number of places.
• Decimal answers stop when the remainder is 0, when a remainder repeats (shown in parentheses), or after 12 decimal places.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 1.5 Divide Whole Numbers. Long division (divide, multiply, subtract, bring down), remainders and checking by multiplying (Examples 1.61–1.66).
2. OpenStax (Rice University), Prealgebra 2e, 5.2 Decimal Operations. Dividing decimals: make the divisor whole by moving both decimal points (Example 5.21: −2.89 ÷ 3.4 = −0.85; Example 5.22: −25.65 ÷ −0.06 = 427.5).

Last reviewed November 2, 2026. To turn a fraction into a decimal directly, use the fraction to decimal calculator.