Long division by a one-digit divisor

In Year 3 you divided small numbers in your head: 24 ÷ 3, 36 ÷ 4. Now the numbers get bigger and memory isn't enough. That is where long division comes in — a step-by-step routine that splits the number digit by digit, from left to right.

What division actually means

Dividing means sharing equally or finding how many times the divisor fits inside the dividend.

84 ÷ 4 can be read in two ways:

• "Share 84 sweets among 4 children. How many does each child get?"
• "How many fours can you take out of 84?"

Both readings give the same answer: 21.

Three words you will use

Work left to right

Unlike column addition, where you start on the right (the ones), long division always starts on the left — at the highest place of the dividend.

84 ÷ 4 = ?

1. Look at the first digit: 8.
2. Ask "How many times does 4 fit into 8?" Answer: 2.
3. Write 2 as the first digit of the quotient.
4. Multiply 4 × 2 = 8 and subtract: 8 − 8 = 0.
5. Bring down the next digit: 4.
6. Ask "How many times does 4 fit into 4?" Answer: 1.
7. Write 1 in the quotient. 4 × 1 = 4, subtract: 4 − 4 = 0.

Done. 84 ÷ 4 = 21, with no remainder.

When a remainder shows up

Not every division is exact.

25 ÷ 4 = ?

4 fits into 25 six times (because 4 × 6 = 24). One is left over.

We write 25 ÷ 4 = 6 remainder 1, or 6 r 1 for short.

The remainder is always smaller than the divisor. If it were equal or larger, the divisor would fit one more time and the quotient would be one bigger.

What you'll learn

• Step-by-step procedure — the whole algorithm
• Division with a remainder — when it doesn't divide exactly
• Estimating and checking — make sure you got it right
• For parents — tips for grown-ups

Try it out

• ➗ Long division — step by step
• 🔢 Division with remainder — whole-number answer plus a remainder
• 🎯 Divide by 10, 100, 1 000 — quick divisions by round divisors