Division by a two-digit number

Long division is the way to divide larger numbers without a calculator. By fifth grade you know how to divide by a one-digit number; the next step is to divide by a two-digit divisor like 23, 56 or 99. The recipe is exactly the same — you just have to estimate each digit of the quotient a little more carefully.

What you will learn

In this topic you will work through:

The principle of long division – why we divide one chunk at a time and where the remainder comes from.
Step-by-step procedure – the exact moves for each digit of the quotient.
Worked examples and common mistakes – fully solved problems and the slip-ups to watch for.

A first look

Take $1234 : 56$ . We pull off the smallest left-hand chunk of $1234$ that is at least $56$ — that is $123$ . Then $123 : 56 = 2$ (because $2 \times 56 = 112$ and $3 \times 56 = 168$ which is too big). Subtract: $123 - 112 = 11$ . Bring down the next digit, $4$ : now we have $114$ . And $114 : 56 = 2$ again, with $114 - 112 = 2$ left over. So $1234 : 56 = 22$ remainder $2$ .

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

Why is this useful?

Long division shows up wherever you want to share something equally or to find how many times one number fits into another. It is also a foundation for working with fractions, decimals, and percentages later on.

Difficulty levels

The interactive exercise generates problems at three levels — they all use a two-digit divisor:

easy — 2-digit dividend, 1-digit quotient (one division step).
medium — 3-digit dividend, 2-digit quotient (two division steps).
hard — 4-digit dividend, 3-digit quotient (three division steps).

Practise

When you are ready, open the interactive exercise:

Long division by a two-digit number – generates a two-digit divisor and a 2- to 4-digit dividend, with empty fields for every multiple of the divisor and for the final remainder.

Division by a two-digit number – complete guide