Long division is a way to divide a big number by working along it one digit at a time, writing each step underneath. Every step is the same four moves: divide, multiply, subtract, bring down. If you can do those, you can divide any number by any other.

The words

In 17 ÷ 5 = 3 remainder 2:

  • the dividend is the number being divided, 17;
  • the divisor is the number you divide by, 5;
  • the quotient is the answer, 3;
  • the remainder is what’s left over, 2.

Setting it out

Draw a bracket. The number you’re dividing goes inside it, the number you’re dividing by goes outside on the left, and the answer goes on top, one digit at a time.

    238    the answer goes here
  ┌─────
4 │ 952    952 divided by 4

Keep your columns straight. Each digit of the answer sits directly above the digit you were working on, and that’s what keeps the hundreds, tens and ones in the right places. Squared paper helps a lot.

The four steps

  1. Divide. How many times does the divisor go into the number you’re looking at? Write that digit on top.
  2. Multiply. Multiply that digit by the divisor and write the result underneath.
  3. Subtract. Take it away to find what’s left.
  4. Bring down. Bring the next digit down beside what’s left, and go back to step 1.

Stop when there are no digits left to bring down. Whatever is left at the bottom is the remainder. Some people remember the order with the family: Dad, Mum, Sister, Brother.

Example 1: 952 ÷ 4

    238
  ┌─────
4 │ 952
  − 8
    ─
    15
  − 12
    ──
     32
   − 32
     ──
      0
  1. Start at the left with the 9. 4 goes into 9 twice (2 × 4 = 8). Write 2 on top, above the 9. Subtract: 9 − 8 = 1.
  2. Bring down the 5 to make 15. 4 goes into 15 three times (3 × 4 = 12). Write 3 on top, above the 5. Subtract: 15 − 12 = 3.
  3. Bring down the 2 to make 32. 4 goes into 32 eight times (8 × 4 = 32). Write 8 on top, above the 2. Subtract: 32 − 32 = 0.
  4. There are no more digits to bring down and nothing is left over, so the answer is exactly 238.

Example 2: a remainder, 1,357 ÷ 6

     226
  ┌──────
6 │ 1357
  − 12
    ──
     15
   − 12
     ──
      37
    − 36
      ──
       1
  1. 6 doesn’t go into 1, so start with the first 2 digits: 13. 6 goes into 13 twice (2 × 6 = 12). Write 2 on top, above the 3. Subtract: 13 − 12 = 1.
  2. Bring down the 5 to make 15. 6 goes into 15 twice (2 × 6 = 12). Write 2 on top, above the 5. Subtract: 15 − 12 = 3.
  3. Bring down the 7 to make 37. 6 goes into 37 six times (6 × 6 = 36). Write 6 on top, above the 7. Subtract: 37 − 36 = 1.
  4. There are no more digits to bring down. 1 is left over, so the answer is 226 remainder 1.

Notice where the first digit of the answer went: above the 3, not above the 1, because the first number we could divide was 13.

Example 3: a zero in the answer, 2,436 ÷ 12

      203
   ┌──────
12 │ 2436
   − 24
     ──
       36
     − 36
       ──
        0
  1. 12 doesn’t go into 2, so start with the first 2 digits: 24. 12 goes into 24 twice (2 × 12 = 24). Write 2 on top, above the 4. Subtract: 24 − 24 = 0.
  2. Bring down the 3. 12 doesn’t go into 3, so write 0 on top, above the 3.
  3. Bring down the 6 to make 36. 12 goes into 36 three times (3 × 12 = 36). Write 3 on top, above the 6. Subtract: 36 − 36 = 0.
  4. There are no more digits to bring down and nothing is left over, so the answer is exactly 203.

Step 2 is the one people miss. Every digit you bring down needs a digit on top, even when that digit is 0. Leave it out and you get 23 instead of 203.

Example 4: dividing by a two-digit number, 7,488 ÷ 32

The steps don’t change, but the dividing is harder to do in your head. Make it easy: before you start, write out the first few multiples of 32 down the side of the page.

32, 64, 96, 128, 160, 192, 224, 256, 288

Now each “how many times does it go?” is just a matter of finding the biggest one that fits.

      234
   ┌──────
32 │ 7488
   − 64
     ──
     108
   −  96
     ───
      128
    − 128
      ───
        0
  1. 32 doesn’t go into 7, so start with the first 2 digits: 74. 32 goes into 74 twice (2 × 32 = 64). Write 2 on top, above the 4. Subtract: 74 − 64 = 10.
  2. Bring down the 8 to make 108. 32 goes into 108 three times (3 × 32 = 96). Write 3 on top, above the 8. Subtract: 108 − 96 = 12.
  3. Bring down the 8 to make 128. 32 goes into 128 four times (4 × 32 = 128). Write 4 on top, above the 8. Subtract: 128 − 128 = 0.
  4. There are no more digits to bring down and nothing is left over, so the answer is exactly 234.

A rough guess first tells you whether the answer is sensible: 7,488 ÷ 32 is close to 7,500 ÷ 30, which is 250. An answer of 234 fits. An answer of 23 or 2,340 would mean a slip somewhere.

What to do with the remainder

There are three ways to write the same answer. Take 25 ÷ 4:

  • As a remainder: 6 remainder 1.
  • As a fraction: put the remainder over the divisor. 6¼.
  • As a decimal: keep dividing. 6.25.

Which one you want depends on the question. Sharing 25 lollies among 4 children is 6 each with 1 left over. Cutting a 25 cm ribbon into 4 equal pieces gives 6.25 cm each.

Carrying on into decimals

To keep going, put a decimal point after the number you’re dividing and write some zeros after it. Put a decimal point in the answer directly above. Then carry on exactly as before, bringing down the zeros.

     6.25
  ┌───────
4 │ 25.00
  − 24
    ──
     1 0
   −   8
     ───
       20
     − 20
       ──
        0

4 goes into 25 six times, leaving 1. Bring down a 0 to make 10: 4 goes twice, leaving 2. Bring down another 0 to make 20: 4 goes five times, leaving nothing. So 25 ÷ 4 = 6.25.

Sometimes it never finishes. Try 10 ÷ 3: you get 3, then a remainder of 1, bring down a 0 to make 10 again, and you’re back where you started. The answer is 3.333… with the 3 repeating forever. That’s called a recurring decimal, written with a dot over the digit that repeats. As soon as you see a remainder you’ve already had, you know the digits will repeat from there.

Check your answer

Division undoes multiplication, so multiply back:

answer × divisor + remainder = the number you started with

For example 2: 226 × 6 = 1,356, plus the remainder 1 makes 1,357. Correct.

Where it usually goes wrong

  • A missing zero. If the divisor doesn’t go, you still write 0 on top before bringing down the next digit.
  • Wandering columns. A digit written one place too far left or right changes the answer by ten times.
  • A remainder that’s too big. After each subtraction, what’s left must be smaller than the divisor. If it isn’t, the digit you wrote on top was too small.
  • A subtraction that won’t work. If the number you’re taking away is bigger than the one above it, the digit on top was too big.
  • Bringing down two digits at once. One digit comes down per step, and each one gets a digit on top.

Short division: the same thing, written smaller

When you’re dividing by a number whose times table you know, you can do the multiplying and subtracting in your head and write only what’s left over, as a small digit in front of the next one:

    2 3 8
  ┌───────
4 │ 9¹5³2

4 into 9 goes 2, with 1 over: write the small 1 in front of the 5 to make 15. 4 into 15 goes 3, with 3 over: write the small 3 in front of the 2 to make 32. 4 into 32 goes 8. It’s the same sum as example 1 in a third of the space. Long division is better once the divisor is too big to do in your head.

It’s set out differently in other countries

The layout on this page is the one taught in Australia, Britain and the United States. In much of Europe and Latin America the divisor is written to the right of the number being divided, with the answer underneath it. The arithmetic is exactly the same; only the places you write things change. If a relative learned it another way, their answer will still match yours.

Common questions

What are the steps of long division?
Divide, multiply, subtract, bring down. Divide the divisor into the first part of the number, multiply to see how much that uses up, subtract to find what is left, then bring down the next digit and repeat until there are no digits left.
How do you check a long division answer?
Multiply the answer by the number you divided by, then add the remainder. You should get the number you started with. For 1,357 ÷ 6 = 226 remainder 1, check that 226 × 6 + 1 = 1,357.
What do you do when the divisor doesn’t go into the number?
Write a 0 in the answer above that digit, then bring down the next digit and try again. Forgetting that 0 is the most common mistake in long division.
What is the difference between long division and short division?
They are the same method. In short division you do the multiplying and subtracting in your head and write only the small carried remainders. In long division you write every step underneath, which is easier when you are dividing by a number bigger than 12.
What are the dividend, divisor, quotient and remainder?
The dividend is the number being divided. The divisor is the number you divide by. The quotient is the answer, and the remainder is whatever is left over. In 17 ÷ 5 = 3 remainder 2, the dividend is 17, the divisor 5, the quotient 3 and the remainder 2.

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