Step-by-step procedure

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 $1234:56$:

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 — $123\ge 56$.

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 ($123$).

Step 4 – subtract

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

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: $114-112=2$.

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.

Read more

• Division by a two-digit number – guide
• The principle of long division
• Worked examples and common mistakes

Practise

• Long division by a two-digit number