Division of 3-Digit by 1-Digit
Division of a 3-digit number by a 1-digit number extends the long division method to numbers in the hundreds. The same four steps — Divide, Multiply, Subtract, Bring down — are used, but now there are more digits to process.
This is a core skill in Class 4 and prepares students for dividing even larger numbers in Class 5.
What is Division of 3-Digit by 1-Digit - Class 4 Maths (Division (Grade 4))?
When a number between 100 and 999 (the dividend) is divided by a number between 1 and 9 (the divisor), the quotient can be a 2-digit or 3-digit number.
- If the hundreds digit is greater than or equal to the divisor → quotient is 3 digits.
- If the hundreds digit is less than the divisor → quotient is 2 digits.
Division of 3-Digit by 1-Digit Formula
Dividend = Divisor × Quotient + Remainder
Solved Examples
Example 1: Example 1: Exact Division (3-Digit Quotient)
Problem: Divide 846 ÷ 2
Solution:
Step 1: 8 ÷ 2 = 4. Write 4. Subtract: 8 − 8 = 0.
Step 2: Bring down 4. 4 ÷ 2 = 2. Write 2. Subtract: 4 − 4 = 0.
Step 3: Bring down 6. 6 ÷ 2 = 3. Write 3. Subtract: 6 − 6 = 0.
Answer: 846 ÷ 2 = 423
Example 2: Example 2: 2-Digit Quotient (Hundreds Digit < Divisor)
Problem: Divide 259 ÷ 7
Solution:
2 < 7, so take 25.
25 ÷ 7 = 3 (7 × 3 = 21). Subtract: 25 − 21 = 4.
Bring down 9 → 49. 49 ÷ 7 = 7 (7 × 7 = 49). Subtract: 49 − 49 = 0.
Answer: 259 ÷ 7 = 37
Example 3: Example 3: Division with Remainder
Problem: Divide 523 ÷ 4
Solution:
5 ÷ 4 = 1 (4 × 1 = 4). Subtract: 5 − 4 = 1.
Bring down 2 → 12. 12 ÷ 4 = 3 (4 × 3 = 12). Subtract: 12 − 12 = 0.
Bring down 3. 3 ÷ 4 = 0 (4 × 0 = 0). Remainder = 3.
Answer: 523 ÷ 4 = 130 remainder 3
Check: 4 × 130 + 3 = 520 + 3 = 523 ✓
Example 4: Example 4: Zero in the Quotient
Problem: Divide 918 ÷ 9
Solution:
9 ÷ 9 = 1. Subtract: 9 − 9 = 0.
Bring down 1. 1 ÷ 9 = 0 (write 0 in quotient). Remainder = 1.
Bring down 8 → 18. 18 ÷ 9 = 2. Subtract: 18 − 18 = 0.
Answer: 918 ÷ 9 = 102
Example 5: Example 5: Word Problem (Equal Distribution)
Problem: A school has 432 books. They are divided equally into 6 shelves. How many books are on each shelf?
Solution:
432 ÷ 6
4 < 6 → take 43. 43 ÷ 6 = 7 (6 × 7 = 42). Subtract: 43 − 42 = 1.
Bring down 2 → 12. 12 ÷ 6 = 2. Subtract: 12 − 12 = 0.
Answer: Each shelf has 72 books.
Example 6: Example 6: Word Problem (Grouping with Remainder)
Problem: Rahul has 350 stickers. He puts 8 stickers on each page of his album. How many pages does he fill? How many stickers are left?
Solution:
350 ÷ 8
35 ÷ 8 = 4 (8 × 4 = 32). Subtract: 35 − 32 = 3.
Bring down 0 → 30. 30 ÷ 8 = 3 (8 × 3 = 24). Subtract: 30 − 24 = 6.
Quotient = 43, Remainder = 6
Answer: Rahul fills 43 pages with 6 stickers left.
Example 7: Example 7: Division of a Multiple of 100
Problem: Divide 600 ÷ 8
Solution:
6 < 8 → take 60. 60 ÷ 8 = 7 (8 × 7 = 56). Subtract: 60 − 56 = 4.
Bring down 0 → 40. 40 ÷ 8 = 5 (8 × 5 = 40). Subtract: 40 − 40 = 0.
Answer: 600 ÷ 8 = 75
Example 8: Example 8: Distance Word Problem
Problem: Priya drives 456 km in 3 days, covering equal distance each day. How far does she drive daily?
Solution:
456 ÷ 3
4 ÷ 3 = 1 (3 × 1 = 3). Subtract: 4 − 3 = 1.
Bring down 5 → 15. 15 ÷ 3 = 5 (3 × 5 = 15). Subtract: 15 − 15 = 0.
Bring down 6. 6 ÷ 3 = 2 (3 × 2 = 6). Subtract: 6 − 6 = 0.
Answer: Priya drives 152 km daily.
Example 9: Example 9: Checking Division
Problem: Verify that 745 ÷ 9 = 82 remainder 7.
Solution:
Check: 9 × 82 + 7 = 738 + 7 = 745 ✓
Answer: The division is correct.
Example 10: Example 10: Money Word Problem
Problem: Dev saves ₹672 in 4 months. If he saves the same amount each month, how much does he save per month?
Solution:
672 ÷ 4
6 ÷ 4 = 1 (4 × 1 = 4). Subtract: 6 − 4 = 2.
Bring down 7 → 27. 27 ÷ 4 = 6 (4 × 6 = 24). Subtract: 27 − 24 = 3.
Bring down 2 → 32. 32 ÷ 4 = 8 (4 × 8 = 32). Subtract: 32 − 32 = 0.
Answer: Dev saves ₹168 per month.
Real-World Applications
Dividing 3-digit numbers by 1-digit numbers is used in:
- Fair sharing: Distributing items equally among groups.
- Averaging: Finding average marks or scores.
- Measurement: Converting a total distance or weight into equal parts.
- Budgeting: Dividing monthly expenses equally across weeks.
Key Points to Remember
- Follow the DMSB steps: Divide, Multiply, Subtract, Bring down.
- If the hundreds digit is less than the divisor, start by dividing the first two digits.
- Write 0 in the quotient when a brought-down number is less than the divisor.
- The remainder must always be less than the divisor.
- Check: Divisor × Quotient + Remainder = Dividend.
- The quotient can be a 2-digit or 3-digit number.
Practice Problems
- Divide 564 ÷ 3.
- Find the quotient and remainder: 739 ÷ 8.
- Neha distributes 315 chocolates equally among 5 children. How many does each child get?
- Divide 804 ÷ 4. Is there a zero in the quotient?
- A rope of length 975 cm is cut into 9 equal pieces. How long is each piece? Is there any rope left?
- Divide 500 ÷ 6 and check your answer.
- Arjun reads 252 pages in 7 days, reading the same number of pages each day. How many pages does he read daily?
- Find 888 ÷ 8.
Frequently Asked Questions
Q1. How do I know if the quotient will be 2 digits or 3 digits?
Compare the hundreds digit with the divisor. If the hundreds digit is greater than or equal to the divisor, the quotient has 3 digits. If it is less, the quotient has 2 digits.
Q2. Why do I sometimes get 0 in the middle of the quotient?
This happens when the number formed after bringing down a digit is still smaller than the divisor. For example, in 918 ÷ 9, after dividing 9, you bring down 1, and since 1 < 9, the quotient digit is 0.
Q3. What is the largest remainder possible when dividing by 7?
The largest remainder is 6, which is one less than the divisor. The remainder is always between 0 and (divisor − 1).
Q4. Can I use estimation before dividing?
Yes. Round the dividend to the nearest hundred. For example, to estimate 523 ÷ 4, round 523 to 520. Then 520 ÷ 4 = 130. The actual answer (130 R 3) is close.
Q5. How do I handle a 3-digit number ending in zero?
Treat the zero like any other digit. Bring it down and divide. For example, in 420 ÷ 6: 42 ÷ 6 = 7, bring down 0, 0 ÷ 6 = 0. Answer: 70.
Q6. Is this different from dividing a 2-digit by 1-digit?
The method is the same (DMSB), but with one extra step since there is an additional digit to process. The quotient can also be larger.
Q7. What if I get a remainder at the end?
Write the quotient with 'remainder' (or R). For example, 523 ÷ 4 = 130 R 3. In word problems, interpret the remainder based on context — sometimes you round up (need one more box).
Q8. Is 3-digit by 1-digit division in the NCERT Class 4 syllabus?
Yes. NCERT Class 4 Maths covers division of numbers up to 3 digits by single-digit divisors using the long division method.
