Long Division — Step-by-Step Method with Examples

Long division is a by-hand way to divide one whole number by another using a repeatable four-step cycle: divide, multiply, subtract, and bring down. Once that cycle clicks, most problems reduce to careful place value and careful subtraction.

When to use it

Long division earns its keep 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 drives decimal division and converting some fractions into decimals — the setup shifts slightly, but the divide-multiply-subtract-bring-down rhythm stays the same.

The core idea is decomposition: instead of demanding the whole quotient at once, you repeatedly ask how many times the divisor fits 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, you fold in the next digit and try again.

The steps, in order

1. Choose the first workable digits. Start from the left and take the smallest leading portion of the dividend 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 no digits remain.

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

Full worked example: $156 \div 12$

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

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

Multiply.

Write $12$ under $15$.

Subtract.

so $3$ is left at this stage.

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

Repeat. $12$ goes into $36$ three times, so write $3$ next to the first quotient digit, then multiply and subtract again:

No digits remain, so

To check, multiply the quotient by the divisor:

The product matches the dividend, so the quotient is correct. When there is a remainder, verify with

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

Where each step traps people, plus a self-check

Step one traps people who start with too few digits: if the divisor is larger than the current digit, do not divide yet — fold in the next digit. In $156 \div 12$, starting from $1$ alone is wrong because $12$ does not fit into $1$. Step two traps those who misplace a quotient digit; each one should line up with the last digit of the part of the dividend you just used, or the rest of the work drifts. Step five traps anyone who forgets to bring down — after every subtraction, ask whether another digit remains before stopping.

For your own pass, try $168 \div 14$ by hand, then check it by multiplication. For one step further, take a remainder problem such as $173 \div 12$ and verify it with $12 \times q + r$.