Long Division Step by Step

Learn long division using the bus stop method — with step-by-step worked examples from simple to challenging, including dealing with remainders.

Long division is the method for dividing big numbers that don't split evenly in your head. The most common method taught in schools is the bus stop method— it's called that because the layout looks like a bus stop shelter.

The Bus Stop Method — Step by Step

Let's break it down into simple steps. The key idea: divide, multiply, subtract, bring down.

Worked Example 1 — 845 ÷ 5

5 into 8 = 1 remainder 3. Write 1 above the 8.
Bring the 3 next to the 4 → 34. 5 into 34 = 6 remainder 4. Write 6 above the 4.
Bring the 4 next to the 5 → 45. 5 into 45 = 9 remainder 0. Write 9 above the 5.
Answer: 169

Check: 169 × 5 = 845 ✓

Worked Example 2 — 3,276 ÷ 12

12 into 3 → doesn't go. Look at 32 instead. 12 into 32 = 2 remainder 8.
Bring down the 7 → 87. 12 into 87 = 7 remainder 3 (because 12 × 7 = 84).
Bring down the 6 → 36. 12 into 36 = 3 remainder 0.
Answer: 273

Check: 273 × 12 = 3,276 ✓

Dealing with Remainders

Sometimes it doesn't divide exactly. You can express the remainder in three ways:

As a remainder: 17 ÷ 5 = 3 remainder 2
As a fraction: 17 ÷ 5 = 3 and 2/5
As a decimal: 17 ÷ 5 = 3.4

Worked Example 3 — 4,589 ÷ 14

14 into 45 = 3 remainder 3 (14 × 3 = 42)
Bring down 8 → 38. 14 into 38 = 2 remainder 10 (14 × 2 = 28)
Bring down 9 → 109. 14 into 109 = 7 remainder 11 (14 × 7 = 98)
Answer: 327 remainder 11 (or 327 and 11/14)

Check: 327 × 14 + 11 = 4,578 + 11 = 4,589 ✓

Short Division — The Quick Version

Short division is the same idea but you do the working in your head and write remainders as small carry digits. It's faster once you're confident, but long division is safer for bigger divisors.

Always Check with Multiplication

The best thing about division is that it's easy to check: answer × divisor should give you the original number.

Try It Yourself

468 ÷ 6 (Answer: 78)
1,536 ÷ 8 (Answer: 192)
2,347 ÷ 15 (Answer: 156 remainder 7)