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Long division, explained step by step

A long division shares out a large number using a division bracket. The method comes down to four steps that repeat: divide, multiply, subtract, bring down. We explain it in detail, including the remainder.

Ages 8–116 min read

Setting out a division

Write the dividend (the number to be shared) on the left, and the divisor (how many parts you share into) on the right, separated by a bracket. The quotient (the answer) is written next to the divisor.

684 ÷ 4 = 171

The method in 4 steps

You work through the digits of the dividend one by one, from left to right. At each step, you repeat the same actions:

  1. Divide: how many times does the divisor fit into the current number? That digit goes to the quotient.
  2. Multiply: multiply this digit by the divisor.
  3. Subtract: take away this product to find what is left.
  4. Bring down: bring the next digit of the dividend down next to the remainder, and start again.
TipA memory aid: "Does McDonald's Sell Burgers?" → Divide, Multiply, Subtract, Bring down.

A full example: 684 ÷ 4

  1. 6 ÷ 4: 4 fits 1 time into 6. Write 1 in the quotient. 1 × 4 = 4, and 6 − 4 = 2.
  2. Bring down the 8 → 28. 28 ÷ 4 = 7 (because 7 × 4 = 28). Write 7. 28 − 28 = 0.
  3. Bring down the 4 → 4. 4 ÷ 4 = 1. Write 1. 4 − 4 = 0.

Nothing is left: the quotient is 171 and the remainder is 0. The division comes out exactly.

Division with a remainder

Often the sharing does not come out exactly: a remainder is left over. This remainder is always smaller than the divisor. Example: 754 ÷ 5.

754 ÷ 5 = 150, remainder 4

  1. 7 ÷ 5 = 1, remainder 2 (because 1 × 5 = 5, and 7 − 5 = 2).
  2. Bring down the 5 → 25. 25 ÷ 5 = 5, remainder 0.
  3. Bring down the 4 → 4. 5 does not fit into 4: write 0 in the quotient. The remainder is 4.
Watch outWhen the divisor does not fit into the number you brought down, don't forget to write a 0 in the quotient before bringing down the next digit. It's the most common mistake.

Checking your answer

A division is checked with a multiplication: quotient × divisor + remainder = dividend. Here: 150 × 5 + 4 = 750 + 4 = 754 ✓. If it doesn't match, there is a mistake (often a forgotten 0 in the quotient).

Worked exercises

96 ÷ 3
9 ÷ 3 = 3. Bring down the 6 → 6 ÷ 3 = 2 → 32, remainder 0.
85 ÷ 4
8 ÷ 4 = 2, remainder 0. Bring down the 5 → 5 ÷ 4 = 1, remainder 1 → 21, remainder 1. Check: 21 × 4 + 1 = 85 ✓.
612 ÷ 6
6 ÷ 6 = 1. Bring down the 1 → 6 does not fit into 1: write 0. Bring down the 2 → 12 ÷ 6 = 2 → 102, remainder 0.

Now it's your turn!

On EasyMaths, your child practises long division with varied exercises and instant marking. The first exercises are free.

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Frequently asked questions

How do you set out a long division?

Write the dividend on the left and the divisor on the right, separated by a bracket. Divide the digits of the dividend one by one, from left to right, and write the quotient next to the divisor.

What is the long division method?

You repeat four steps: divide, multiply, subtract, bring down. Divide the current number by the divisor, multiply the digit you found by the divisor, subtract, then bring down the next digit.

What is the remainder of a division?

It is what cannot be shared any further. It is always smaller than the divisor. When the remainder is 0, the division comes out exactly.

At what age do children learn long division?

Division by a single digit is learned around ages 8 to 9; division by a two-digit number is practised around ages 10 to 12.

Continue with…

Long multiplicationThe inverse operation, to check your divisions Column subtractionBorrowing, used at each step of the division Times tablesEssential for dividing quickly and correctly All maths lessonsPrimary school, ages 5 to 12