Long Division

What Is Long Division?

Long division is a method for dividing a large number (the dividend) by another number (the divisor) when mental methods are too difficult. It works digit by digit, from left to right.

The four steps repeat over and over:

Divide — how many times does the divisor fit?
Multiply — multiply the result back
Subtract — find the remainder
Bring down — bring the next digit down

Note

Long division is the foundation of many advanced maths skills, including dividing algebraic expressions and working with decimals.

Step-by-Step Example

Calculate $756 \div 4$

Step 1: Look at the first digit: $7 \div 4 = 1$ remainder $3$ . Write $1$ above.

Step 2: Bring down the next digit ( $5$ ). New number: $35$ .

Step 3: $35 \div 4 = 8$ remainder $3$ . Write $8$ above.

Step 4: Bring down the next digit ( $6$ ). New number: $36$ .

Step 5: $36 \div 4 = 9$ remainder $0$ . Write $9$ above.

$756 \div 4 = \mathbf{189}$

Check: $189 \times 4 = 756$ ✓

Tip

Always check your answer by multiplying the quotient by the divisor. If you get the original dividend, you are correct!

Example With a Remainder

Calculate $983 \div 6$

$9 \div 6 = 1$ rem $3$ . Bring down $8$ → $38$
$38 \div 6 = 6$ rem $2$ . Bring down $3$ → $23$
$23 \div 6 = 3$ rem $5$

$983 \div 6 = \mathbf{163} \text{ remainder } 5$

Or as a mixed number: $163\frac{5}{6}$

Check: $163 \times 6 + 5 = 978 + 5 = 983$ ✓

Warning

If the first digit of the dividend is smaller than the divisor, look at the first two digits together. For $\mathbf{3}64 \div 7$ : $3 < 7$ , so look at $36 \div 7 = 5$ remainder $1$ .

Real world: sharing costs equally

A group of 6 friends shares a holiday cottage costing €1272. Each person pays $1272 \div 6 = 212$ . Using long division: $12 \div 6 = 2$ , bring down $7$ → $7 \div 6 = 1$ rem $1$ , bring down $2$ → $12 \div 6 = 2$ . Each friend owes exactly €212.

Real world: splitting factory output into crates

A factory produces 875 bottles and packs them into crates of 5. $875 \div 5 = 175$ crates exactly. The warehouse manager uses long division to calculate how many crates are needed and whether any bottles will be left over.

Real world: computing unit prices

A box of 8 tins of soup costs €5.60. Price per tin $= 560\text{ p} \div 8 = 70\text{ p}$ . Long division (or mental short division) turns a total price into a unit price, allowing consumers to compare value for money across different pack sizes.

Tip Always multiply your answer back by the divisor to check. If the product matches the dividend (with remainder added), your division is correct.

Practice Problems

Calculate $648 \div 3$.

Show answer

$6 \div 3 = 2$, $4 \div 3 = 1$ rem $1$, bring down: $14 \div 3 = 4$ rem $2$. Wait — let's be careful: $6 \div 3 = 2$; bring $4$, $4 \div 3 = 1$ rem $1$; bring $8$, $18 \div 3 = 6$. Answer: $216$. Check: $216 \times 3 = 648$ ✓

Calculate $875 \div 5$.

Show answer

$8 \div 5 = 1$ rem $3$; bring $7$ → $37 \div 5 = 7$ rem $2$; bring $5$ → $25 \div 5 = 5$. Answer: $175$. Check: $175 \times 5 = 875$ ✓