Stop with a remainder
1,456 ÷ 32 = 45 remainder 16. After the 6 has been used, 16 remains. It is smaller than 32, so this is a complete remainder answer.
Divide, subtract, then continue
Before this page: be confident with multiplication facts, column subtraction and division by a one-digit number using short division.
Long division is used here when the divisor has two digits. It makes each subtraction visible, so the remainder from one stage becomes the starting amount for the next.
List the multiples first
At each stage, choose the greatest multiple of the divisor that does not exceed the current amount. Listing the first nine multiples makes that choice visible and reduces guessing.
1 × 2323
2 × 2346
3 × 2369
4 × 2392
5 × 23115
6 × 23138
7 × 23161
8 × 23184
9 × 23207
For a current amount of 179, choose 161 = 7 × 23. The next multiple, 184, is too large. This proves that the next quotient digit is 7.
A whole-number quotient
Example: calculate 1,794 ÷ 23
1,794 ÷ 23
Set out the calculation
Write 23 outside the bracket and 1,794 inside.
1,794 ÷ 23 = 78
The long-division cycle
Choose, multiply, subtract, bring down
- 1
Choose the greatest listed multiple not exceeding the current amount.
- 2
Write its multiplier in the quotient and its value underneath.
- 3
Subtract to find the remainder. It must be smaller than the divisor.
- 4
Bring down the next written digit and repeat until every digit currently in the dividend has been used.
Keep a zero in the quotient
A quotient zero is needed when the next current amount is smaller than the divisor but another dividend digit still remains. The zero holds that place so every later digit keeps its correct value.
203
15
3045
- Start with 30: 2 × 15 = 30, so write 2 above the 0.
- Bring down 4: 4 is smaller than 15, so write 0 above the 4. There are no groups of 15 in this place.
- Bring down 5: 45 ÷ 15 = 3, so write 3 above the 5.
3,045 ÷ 15 = 203
Choose the form of the answer
Once every original digit has been used, a non-zero remainder creates a choice. Stop if the answer is required as a whole-number quotient with a remainder; append a decimal point and zeroes only if the answer should continue as a decimal.
Continue as a decimal
1,456 ÷ 32 = 45.5. Write 1,456 as 1,456.0, then bring down the appended zero: 160 ÷ 32 = 5.
Continue through the decimal point
Use every digit already written in the dividend first. Place the quotient's decimal point directly above the dividend's point. If a non-zero remainder remains after the final written digit and an exact decimal is required, append a zero and continue.
Example: calculate 68.4 ÷ 24 exactly
68.4 ÷ 24
Set out the calculation
Keep the decimal point on the same place-value boundary in the dividend and quotient.
68.4 ÷ 24 = 2.85
Whether a remainder is sufficient can depend on the question's context, as explained on interpreting a remainder.
Divide two chosen numbers
Choose whether to stop with a remainder or continue as a decimal. Remainder answers use a whole-number dividend. The divisor remains a two-digit integer, and an ellipsis shows when a displayed decimal continues.
Set out 1,456 ÷ 32
Use the listed multiples to choose each quotient digit.
Check by multiplication
Whole-number result
78 × 23 = 1,794, so 1,794 ÷ 23 = 78.
Decimal result
2.85 × 24 = 68.4, so 68.4 ÷ 24 = 2.85.
With a final remainder, multiply the whole-number quotient by the divisor and add the remainder. A failed check often reveals an incorrect multiple, subtraction error or omitted quotient zero.
Long division in context
Equal packing
A supplier places 1,794 bolts equally into 23 crates. Each crate contains 78 bolts.
Equal lengths
A 68.4 m cable is cut into 24 equal lengths. Each length is 2.85 m.
Common mistakes
- Choosing a multiple that is too largeCheck the chosen multiple and the next one. The chosen value must not exceed the current amount.
- Subtracting inaccuratelyKeep digits in their columns and check that each remainder is smaller than the divisor.
- Omitting a zero in the quotientIf the current amount is smaller than the divisor, write 0 in that quotient place before bringing down the next digit.
- Misplacing the decimal pointWrite the quotient's point directly above the dividend's point. The divisor is an integer throughout this page.
Summary
- List the first nine multiples of the two-digit divisor.
- Begin with enough leading dividend digits to make an amount at least as large as the divisor.
- Choose a multiple, write the quotient digit—including 0 when no positive multiple fits—subtract and bring down the next digit.
- Keep decimal points on the same boundary and append zeroes only when a decimal continuation is required.
- Check by multiplying the quotient by the divisor, then adding any final remainder.