Step-by-step procedure for long division

This is the recipe for dividing a 2-, 3- or 4-digit dividend by a two-digit divisor. The steps are the same; only the number of repetitions changes.

Set up the layout

Write the dividend on the left, then a colon, then the divisor, then `=`. After the equals sign you will write the quotient digits one by one. To the right, leave space for "remainder X". Below the dividend, draw a workspace for the partial products and differences.

For $1234 : 56$ :

1234 : 56 = ?

Step 1 – first chunk

Pick the smallest left-hand chunk of the dividend that is at least as large as the divisor. For $1234$ and divisor $56$ :

Just $1$ ? No — too small.
$12$ ? Still too small ( $12 < 56$ ).
$123$ ? Yes — $123 \geq 56$ .

So the first chunk is $123$ .

Step 2 – estimate the quotient digit

We are looking for the largest digit from 1 to 9 that we can multiply by the divisor $56$ such that the result still fits inside $123$ . We try:

$2 \times 56 = 112$ — that fits inside $123$ .
$3 \times 56 = 168$ — that is bigger than $123$ , so too much.

So the right digit is $2$ . Write it as the first digit of the quotient.

Step 3 – multiply and write below

Multiply the divisor by the quotient digit ( $2 \times 56 = 112$ ). Write the product directly under the chunk ( $123$ ).

1234 : 56 = 2…
112

Step 4 – subtract

Draw a small bar and subtract: $123 - 112 = 11$ . Write the difference below the bar.

1234 : 56 = 2…
112
───
 11

Step 5 – bring down the next digit

Bring down the next digit of the dividend (here $4$ ) and append it to the right of the difference. The new chunk is $114$ .

Now repeat steps 2–4 with the new chunk $114$ :

We look for a digit that, multiplied by $56$ , gives a number close to $114$ but not bigger. $2 \times 56 = 112$ — fits nicely; $3 \times 56 = 168$ is too much. The digit is $2$ .
Write $2$ as the next digit of the quotient: the quotient is now $22$ .
Write $112$ below $114$ and subtract: $114 - 112 = 2$ .

1234 : 56 = 22 r. 2
112
───
 114
 112
 ───
   2

Step 6 – stop and read the remainder

When there are no more digits in the dividend to bring down, the last difference is the remainder. Here it is $2$ . Check that it is smaller than the divisor — $2$ is indeed less than $56$ , so we are done.

Final answer: $1234 : 56 = 22$ remainder $2$ .

How many digits will the quotient have?

A handy rule of thumb:

2-digit dividend ÷ 2-digit divisor → 1-digit quotient.
3-digit dividend ÷ 2-digit divisor → 2-digit quotient (when the leading 2 digits of the dividend are at least the divisor).
4-digit dividend ÷ 2-digit divisor → 3-digit quotient (when the leading 2 digits of the dividend are at least the divisor).

The exercise generator uses these patterns so the difficulty grows in clean steps.

Practise

Long division by a two-digit number