Long Division Calculator

Enter a dividend and a divisor. You get the quotient and remainder, the long-division working digit by digit, and the exact decimal result.

Divide with remainder

Quotient and remainder176 R 2
As a mixed number
176 2/7
As a decimal
176.(285714) (digits in brackets repeat forever)
Check
176 × 7 + 2 = 1,234

Working

  1. Bring down 1: 1 is less than 7, so write 0 (or skip) and carry on
  2. Bring down 2 → 12. 12 ÷ 7 = 1; 1 × 7 = 7; 12 − 7 = 5
  3. Bring down 3 → 53. 53 ÷ 7 = 7; 7 × 7 = 49; 53 − 49 = 4
  4. Bring down 4 → 44. 44 ÷ 7 = 6; 6 × 7 = 42; 44 − 42 = 2

The method

  1. Take the digits of the dividend from the left until the number is at least as big as the divisor.
  2. Divide: how many whole times does the divisor fit? Write that digit in the quotient.
  3. Multiply the digit by the divisor and subtract.
  4. Bring down the next digit and repeat.
  5. What is left after the last digit is the remainder.

Worked example

1,234 ÷ 7

  1. 12 ÷ 7 = 1, 1 × 7 = 7, 12 − 7 = 5
  2. Bring down 3 → 53. 53 ÷ 7 = 7, 7 × 7 = 49, 53 − 49 = 4
  3. Bring down 4 → 44. 44 ÷ 7 = 6, 6 × 7 = 42, 44 − 42 = 2

1,234 ÷ 7 = 176 remainder 2, i.e. 176 2/7 = 176.285714285714…

Checking your answer

dividend = quotient × divisor + remainder

176 × 7 + 2 = 1,232 + 2 = 1,234 ✓. The remainder must always be smaller than the divisor.

Remainders as decimals

Dividing further past the decimal point turns the remainder into decimal digits. When the divisor has prime factors other than 2 and 5, the decimal repeats forever: 2/7 = 0.285714285714…, written 0.(285714). The calculator shows the repeating block in brackets.