Long Division — Step-by-Step Method with Examples

Long division is a step-by-step way to divide one whole number by another by hand. If you want to know how to do long division, the repeatable pattern is: divide, multiply, subtract, and bring down.

Once that cycle clicks, most long-division problems become an exercise in place value and careful subtraction.

1. Divide.
2. Multiply.
3. Subtract.
4. Bring down.

What Long Division Means

Long division breaks one large division into smaller, manageable parts. Instead of asking for the whole quotient at once, you ask: how many times does the divisor fit into the current part of the dividend?

That is why you do not always start with the first digit alone. If the divisor is larger than that digit, include the next digit and try again.

Long Division Steps in Order

1. Look at the leftmost part of the dividend that the divisor can actually fit into.
2. Write the quotient digit above that part of the dividend.
3. Multiply that quotient digit by the divisor.
4. Write the product underneath and subtract.
5. Bring down the next digit.
6. Repeat until there are no digits left.

If the final subtraction is not $0$, the amount left over is the remainder.

Worked Example: $156 \div 12$

We want to find $156 \div 12$.

Start from the left. Since $12$ does not fit into $1$, use the first two digits: $15$.

1. Divide

$12$ goes into $15$ one time, so write $1$ in the quotient.

2. Multiply

$$1 \times 12 = 12$$

Write $12$ under $15$.

3. Subtract

$$15 - 12 = 3$$

So the amount left at this stage is $3$.

4. Bring Down

Bring down the next digit, which is $6$, to make $36$.

5. Repeat the Cycle

$12$ goes into $36$ three times, so write $3$ next to the first quotient digit.

Then multiply and subtract again:

$$3 \times 12 = 36$$ $$36 - 36 = 0$$

There are no digits left to bring down, so the division is complete.

$$156 \div 12 = 13$$

How to Check Your Answer

Multiply the quotient by the divisor:

$$13 \times 12 = 156$$

Because the product matches the original dividend, the quotient is correct.

If there is a remainder, use:

$$\text{dividend} = \text{divisor} \times \text{quotient} + \text{remainder}$$

For example, $157 \div 12 = 13$ remainder $1$ because $12 \times 13 + 1 = 157$.

Common Mistakes

Starting with Too Few Digits

If the divisor is larger than the current digit, do not divide yet. Use the next digit too. In $156 \div 12$, starting with $1$ alone would be wrong because $12$ does not fit into $1$.

Misplacing a Quotient Digit

Each quotient digit should line up with the last digit of the part of the dividend you just used. If the placement is off, the rest of the work usually goes off too.

Forgetting to Bring Down the Next Digit

After each subtraction, ask whether there is another digit left in the dividend. If there is, bring it down before you stop.

When Long Division Is Used

Long division is useful when the divisor has two or more digits, when you need to show your reasoning clearly, or when you need an exact quotient and remainder.

The same structure also helps with decimal division and with converting some fractions into decimals. The setup changes a little, but the divide-multiply-subtract-bring-down pattern stays the same.

Try A Similar Problem

Try your own version with $168 \div 14$. Solve it by hand first, then check it by multiplication.

For one more step, try a remainder problem such as $173 \div 12$ and verify it with $12 \times q + r$.