Long Division, NCERT Method: Step by Step
NCERT textbooks write long division with the divisor on the left followed by “)”, the dividend in the middle, and the quotient on the right after “(”, for example 3) 324 (108. The working is written below the dividend, with each product subtracted in turn.
The example below, 324 ÷ 3, is the one printed in the Class 5 NCERT book. It is a good test of the method because a 0 has to be written in the middle of the quotient.
When is long division taught?
- Class 4 (Maths Mela): division by partial quotients, where remainders first appear.
- Class 5 (Maths Mela): long division of 4-digit numbers by 1-digit numbers and 3-digit numbers by 2-digit numbers, with the rule dividend = divisor × quotient + remainder.
Worked example: 324 ÷ 3
3)324(
3)324(108−324−240
Left: the problem. Right: the finished working as it appears in our answer keys.
Step by step
- 1Start with the first digit, 3.
- 2Divide: how many times does 3 go into 3? 1 time, so write 1 in the quotient. Multiply: 1 × 3 = 3. Subtract: 3 − 3 = 0.
- 3Bring down the next digit, 2, to make 2.
- 42 is smaller than 3, so write 0 in the quotient.
- 5Bring down the next digit, 4, to make 24.
- 6Divide: how many times does 3 go into 24? 8 times, so write 8 in the quotient. Multiply: 8 × 3 = 24. Subtract: 24 − 24 = 0.
- 7It divides exactly: the answer is 108.
- 8Check: 3 × 108 = 324.
Common mistakes
- Leaving out the 0: in 324 ÷ 3 the 2 brought down is smaller than 3, so the quotient needs a 0 — the answer is 108, not 18.
- Remainder larger than the divisor: after each subtraction the result must be smaller than the divisor.
- Checking: multiply the divisor by the quotient and add the remainder — you must get the dividend back.
Printable long division practice
- Division with remainders: 3-digit ÷ 2-digitClass 4 · NCERT Maths Mela, Class 4
- Long division: 4-digit ÷ 1-digitClass 5 · NCERT Maths Mela, Class 5
- Long division: 3-digit ÷ 2-digitClass 5 · NCERT Maths Mela, Class 5