Long Division Calculator

Divide two whole numbers using the classic long-division layout. See the quotient, the remainder and the full divide–multiply–subtract–bring-down process, with an option to continue past the decimal point.

What is long division?

Long division is the standard written method for dividing one whole number (the dividend) by another (the divisor) when the numbers are too big to divide in your head. Instead of tackling the whole dividend at once, you work through it one digit at a time from left to right — writing the answer (the quotient) above a horizontal bar and any leftover amount (the remainder) at the bottom. The relationship it enforces at every step is dividend = quotient × divisor + remainder.

Long division, step by step

Every stage of long division cycles through the same four moves on a smaller and smaller piece of the dividend. Below is what each move looks like using 1258 ÷ 7.

1. Divide — how many times does the divisor fit?

Read enough leading digits of the dividend so that the running number is at least as big as the divisor. Ask: how many whole times does the divisor fit in? Write that count above the last digit you used.

q = ⌊current ÷ divisor⌋
currentthe digits you've collected so far·qnext quotient digit written above the bar
     1        
   ─────      
 7 ) 1 2 5 8  
Example
Given
1258 ÷ 7 — start
"12" (since "1" < 7)
Substitute
⌊12 ÷ 7⌋ = 1
Answer
write 1 above the 2

2. Multiply — the divisor times the new quotient digit

Multiply the divisor by the digit you just wrote and place the product directly under the digits you were looking at. This is the largest multiple of the divisor that still fits.

product = q × divisor
qquotient digit from step 1·productwritten under the current digits
     1        
 7 ) 1 2 5 8  
    − 7       
    ───       
Example
Given
q = 1
divisor = 7
Substitute
1 × 7 = 7
Answer
write 7 under the "12"

3. Subtract — find the leftover

Subtract the product from the digits above it and draw a short line. The result is the leftover — always smaller than the divisor, or you chose too small a quotient digit in step 1.

leftover = current − product
leftovermust be less than the divisor
 7 ) 1 2 5 8  
    − 7       
    ───       
      5       
Example
Given
current = 12
product = 7
Substitute
12 − 7 = 5
Answer
5 is the leftover
far

4. Bring down — pick up the next dividend digit

Copy the next unused digit of the dividend down beside the leftover to form the new running number. Return to step 1 with this bigger number and repeat until every dividend digit has been used.

new current = leftover · 10 + next digit
next digitthe next digit of the dividend
     1  7  9  
 7 ) 1 2 5 8  
    − 7       
    ───       
      5 5     
Example
Given
leftover 5
next digit 5
Substitute
5·10 + 5 = 55
then ⌊55 ÷ 7⌋ = 7
Answer
write 7 above the 5
continue to get 179 R 5

Continuing past the decimal point

To turn the remainder into decimals, place a decimal point in the quotient after the last integer digit, then pretend the dividend has ".000…" tacked on. Bring down a zero, divide, and repeat as many times as you need.

append .0
bring down
repeat
Rthe remainder you're extending
  1 7 9 . 7   
 7 ) 1 2 5 8 . 0
              
        5 0   
      − 4 9   
        ───   
          1   
Example
Given
1258 ÷ 7 leaves remainder 5
Substitute
bring down 0 → 50
⌊50 ÷ 7⌋ = 7 remainder 1
Answer
1258 ÷ 7 ≈ 179.7…

Features of this calculator

  • Classic long-division layout with divisor, dividend, quotient and dashes aligned
  • Every subtraction and bring-down shown in the same monospaced grid
  • Whole-number mode returns quotient plus remainder (e.g. 17 ÷ 5 = 3 R 2)
  • Decimal mode continues the division to any number of decimal places
  • Handles leading zeros and multi-digit divisors correctly

Frequently asked questions

+How do I do long division with decimals?

Once you've used every digit of the dividend, put a decimal point in the quotient and start bringing down zeros. Each zero acts like the next digit of the dividend, and the divide-multiply-subtract-bring-down cycle continues normally until the remainder is zero or you decide to stop.

+What do I do when the divisor doesn't go in evenly?

Either stop and record the leftover as a remainder (e.g. 22 ÷ 5 = 4 R 2), or continue past the decimal point by appending zeros. Both answers are correct — the remainder form is exact, and the decimal form gives an approximation to as many places as you want.

+Why is there a 0 in the middle of my quotient?

Because once you have started writing the quotient, you must write a digit above every dividend digit you process — even when the current number is smaller than the divisor. In that case the divisor fits 0 times, so you write a 0 and immediately bring the next digit down.

+Can I use long division to divide by a multi-digit number?

Yes. The steps don't change — the only harder part is estimating how many times a multi-digit divisor fits into the current number. Trial multiplication or rounding the divisor to the nearest ten can help you pick each quotient digit.

Related calculators