Long division calculator
Enter two whole numbers, get the quotient, remainder and every step.
How do I do long division?
Divide digit by digit from the left: see how many times the divisor fits, write that digit, subtract, bring down the next digit and repeat. 1,234 ÷ 7: 12 ÷ 7 = 1 r 5, 53 ÷ 7 = 7 r 4, 44 ÷ 7 = 6 r 2 — so 176 remainder 2.
How do I check the answer?
Multiply back and add the remainder: 7 × 176 + 2 = 1,234. If you get the dividend, the division is right.
How do I write the remainder as a fraction or decimal?
Put the remainder over the divisor: 176 r 2 = 176 2/7. As a decimal, keep dividing after the point: 2/7 = 0.285714285714…, so 1,234 ÷ 7 = 176.(285714).
What do the parentheses in the decimal mean?
The digits inside repeat forever: 0.1(6) = 0.1666…, and 3.(142857) = 3.142857142857…. Every fraction ends up either stopping or repeating.
Can I divide by a two-digit number?
Yes — the steps are the same, you just check how many times, say, 24 fits into each part. The calculator shows every step for any whole-number divisor.
What are the dividend, divisor, quotient and remainder?
In 28 ÷ 8 = 3 R4, 28 is the dividend (the number being split), 8 is the divisor, 3 is the quotient and 4 is the remainder, what is left over. The remainder is always smaller than the divisor.
What do I do when the divisor is bigger than the first digit?
Use the first two digits instead. To divide 253 by 4, 4 does not go into 2, so start with 25: 4 goes into 25 six times. If the divisor is also bigger than the first two digits, take three.
How do I divide decimals?
Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. 4.5 ÷ 0.15 becomes 450 ÷ 15 = 30.
How the method works
Long division breaks one big division into a chain of small ones. At each step you take the digits brought down so far, find how many whole times the divisor fits, write that digit in the quotient, multiply, and subtract. The difference is carried forward with the next digit of the dividend appended. When the digits run out, what is left is the remainder. If it is not zero you can continue after a decimal point by adding zeros, and the process either stops or the remainders repeat, which gives a repeating decimal.
Worked example: 8,765 ÷ 12
12 does not go into 8, so take 87: 12 goes into 87 7 times (12 × 7 = 84), leaving 3. Bring down 6 to make 36: 12 goes in 3 times, leaving 0. Bring down 5: 12 does not go into 5, so the last quotient digit is 0 and the remainder is 5. The answer is 730 remainder 5. Check: 12 × 730 + 5 = 8765. Continuing past the point gives 730.41(6), where the 6 repeats forever.
Mistakes to avoid
The most common slip is dropping a zero. In 4,213 ÷ 4 the quotient is 1053: the second step does not divide, and a 0 must be written there or the answer collapses to the wrong size. The second is a remainder that is as big as the divisor, which means the quotient digit was too small; raise it by one. The third is subtraction errors, so verify with multiplication.
Sources: OpenStax, Prealgebra 2e, section 1.5 "Divide Whole Numbers" (terms, steps, zero placeholder, checking by multiplication). Related tools: fraction calculator, decimal to fraction calculator, fraction to percent calculator, ratio calculator.