➗ Division

Grade 5 · Number · Cambridge Primary Stage 5

Division Facts

Related to multiplication tables

÷10, ÷100, ÷1000

Moving digits right

Short Division

Bus stop method step by step

Remainders

As whole numbers or fractions

Divisibility Rules

Quick tests for ÷2, ÷3, ÷5...

1. Division Facts

Division and multiplication are inverse operations. If you know your times tables, you know your division facts!

If 6 × 7 = 42, then 42 ÷ 6 = 7 and 42 ÷ 7 = 6
Division fact families:
3 × 8 = 24 → 24 ÷ 3 = 8 and 24 ÷ 8 = 3
9 × 6 = 54 → 54 ÷ 9 = 6 and 54 ÷ 6 = 9
12 × 7 = 84 → 84 ÷ 12 = 7 and 84 ÷ 7 = 12
💡 To divide, ask yourself: "What times the divisor gives the dividend?"

2. Dividing by 10, 100, 1000

When you divide by 10, 100, or 1000, every digit moves to the right on the place value chart.

÷10 → move digits one place right  |  ÷100 → two places  |  ÷1000 → three places
470 ÷ 10 = 47
4,700 ÷ 100 = 47
47,000 ÷ 1,000 = 47

3,600 ÷ 10 = 360
3,600 ÷ 100 = 36
3,600 ÷ 1,000 = 3.6
💡 Dividing by 10 is the opposite of multiplying by 10. Digits shift right instead of left.

3. Short Division (Bus Stop Method)

For dividing a large number by a 1-digit number, use the bus stop method. Work from left to right.

Write the divisor outside the bus stop, the dividend inside. Divide each digit in turn.
Example: 738 ÷ 6
Step 1: 7 ÷ 6 = 1 remainder 1. Write 1 above, carry the 1.
Step 2: 13 ÷ 6 = 2 remainder 1. Write 2 above, carry the 1.
Step 3: 18 ÷ 6 = 3 remainder 0. Write 3 above.
Answer: 123
6 ) 7³1³8 = 123
💡 Always check your answer by multiplying: 123 × 6 = 738 ✓

4. Remainders

Sometimes numbers don't divide exactly. The amount left over is called the remainder.

Remainder = dividend − (quotient × divisor)
Example: 29 ÷ 4
4 × 7 = 28, which is close to 29.
29 − 28 = 1. So 29 ÷ 4 = 7 remainder 1.

As a fraction: the remainder becomes the numerator, the divisor is the denominator.
29 ÷ 4 = 7¼ (because remainder 1 out of 4 = ¼)

Example: 4,317 ÷ 5 = 863 r 2 → or 863⅖
💡 In word problems, think carefully about what the remainder means. If packing boxes, you might need an extra box for the remainder!

5. Divisibility Rules

These rules let you check if a number divides exactly without calculating.

÷2: the last digit is even (0, 2, 4, 6, 8)
÷3: the sum of all digits is divisible by 3
    e.g. 123: 1+2+3=6, and 6÷3=2 ✓
÷5: the last digit is 0 or 5
÷9: the sum of all digits is divisible by 9
    e.g. 729: 7+2+9=18, and 18÷9=2 ✓
÷10: the last digit is 0
💡 A number divisible by both 2 and 3 is also divisible by 6. A number divisible by both 3 and 9 is divisible by 9 (not necessarily by both individually!).

Example 1 — Short Division (no remainder): 952 ÷ 8

Set up bus stop: 8 ) 9 5 2
9 ÷ 8 = 1 r 1. Write 1, carry 1 → next digit becomes 15.
15 ÷ 8 = 1 r 7. Write 1, carry 7 → next digit becomes 72.
72 ÷ 8 = 9. Write 9.
Answer: 119. Check: 119 × 8 = 952 ✓

Example 2 — Short Division (with remainder): 4,317 ÷ 5

5 ) 4 3 1 7
4 ÷ 5 = 0 r 4. Write 0, carry 4 → 43.
43 ÷ 5 = 8 r 3. Write 8, carry 3 → 31.
31 ÷ 5 = 6 r 1. Write 6, carry 1 → 17.
17 ÷ 5 = 3 r 2. Write 3.
Answer: 863 remainder 2. As a fraction: 863⅖

Example 3 — Division by 10 and 100

8,400 ÷ 10 = 840 (digits move one place right)
8,400 ÷ 100 = 84 (digits move two places right)
8,400 ÷ 1,000 = 8.4 (digits move three places right)
The place value of each digit decreases by the power of 10 you divide by.

Example 4 — Word Problem with Remainder

137 people need to travel by minibus. Each minibus holds 9 people. How many minibuses are needed?
137 ÷ 9 = 15 remainder 2
15 full minibuses + 1 more for the 2 remaining people.
Answer: 16 minibuses (you must round UP when people need transport)

🔬 Visualizer 1 — Short Division Step-by-Step

Enter a number (up to 4 digits) and a 1-digit divisor. See the bus stop method worked out.

🔬 Visualizer 2 — Divisibility Checker

Enter a number and see which divisibility rules it passes.

Exercise 1 — Division Facts & ÷10, ÷100

1. 42 ÷ 6 = ?

2. 54 ÷ 9 = ?

3. 84 ÷ 12 = ?

4. 72 ÷ 8 = ?

5. 110 ÷ 11 = ?

6. 470 ÷ 10 = ?

7. 8,500 ÷ 100 = ?

8. 36,000 ÷ 1,000 = ?

9. 9,600 ÷ 100 = ?

10. 7,200 ÷ 10 = ?

Exercise 2 — Short Division (No Remainder)

1. 738 ÷ 6 = ?

2. 952 ÷ 8 = ?

3. 693 ÷ 9 = ?

4. 848 ÷ 4 = ?

5. 756 ÷ 7 = ?

6. 2,436 ÷ 6 = ?

7. 3,645 ÷ 5 = ?

8. 4,872 ÷ 8 = ?

9. 6,237 ÷ 9 = ?

10. 7,896 ÷ 4 = ?

Exercise 3 — Short Division (With Remainder)

Enter only the whole number quotient (ignore the remainder for now).

1. 29 ÷ 4 = ? (whole number part only)

2. 50 ÷ 7 = ? (whole number part)

3. 4,317 ÷ 5 = ? (whole number part)

4. 835 ÷ 6 = ? (whole number part)

5. 2,749 ÷ 8 = ? (whole number part)

6. 29 ÷ 4 = ? — Enter the remainder only.

7. 50 ÷ 7 = ? — Enter the remainder only.

8. 4,317 ÷ 5 = ? — Enter the remainder only.

9. 835 ÷ 6 = ? — Enter the remainder only.

10. 2,749 ÷ 8 = ? — Enter the remainder only.

Exercise 4 — Divisibility Rules

Enter 1 if the number is exactly divisible, 0 if not.

1. Is 348 divisible by 2? (Enter 1 or 0)

2. Is 345 divisible by 5? (Enter 1 or 0)

3. Is 237 divisible by 3? (digit sum = 12) (Enter 1 or 0)

4. Is 729 divisible by 9? (digit sum = 18) (Enter 1 or 0)

5. Is 4,560 divisible by 10? (Enter 1 or 0)

6. Is 481 divisible by 2? (Enter 1 or 0)

7. Is 246 divisible by 3? (digit sum = 12) (Enter 1 or 0)

8. Is 3,855 divisible by 5? (Enter 1 or 0)

9. Is 2,736 divisible by 9? (digit sum = 18) (Enter 1 or 0)

10. Is 5,431 divisible by 3? (digit sum = 13) (Enter 1 or 0)

Exercise 5 — Division Word Problems

1. 84 sweets are shared equally among 6 friends. How many each?

2. A baker makes 345 rolls and packs them in bags of 5. How many bags?

3. 137 students go on a trip in minibuses holding 9 each. How many minibuses are needed?

4. A rope 4,872 cm long is cut into 8 equal pieces. How long is each piece in cm?

5. £2,436 prize money is shared equally between 6 winners. How much each in £?

6. 3,645 pages of books to pack into boxes of 5. How many boxes?

7. A farmer has 756 eggs and packs them in boxes of 7. How many boxes?

8. 5,000 chairs set out in rows of 9. How many complete rows? (whole number only)

9. 36,000 ml of juice poured into 1,000 ml bottles. How many bottles?

10. A machine fills 8 bottles per second. How many seconds to fill 2,248 bottles?

🏋️ Practice — 20 Questions

1. 63 ÷ 9 = ?

2. 96 ÷ 8 = ?

3. 5,700 ÷ 100 = ?

4. 648 ÷ 6 = ?

5. 2,835 ÷ 5 = ?

6. Is 4,725 divisible by 9? (1 = yes, 0 = no)

7. 3,528 ÷ 7 = ?

8. 900 ÷ 6 = ?

9. 47 ÷ 5 — what is the remainder?

10. 4,800 ÷ 1,000 = ?

11. 132 chairs in rows of 4. How many rows?

12. 7,623 ÷ 9 = ?

13. Is 351 divisible by 3? (1 = yes, 0 = no)

14. 2,248 ÷ 8 = ?

15. 54 ÷ 6 = ?

16. 250 students in groups of 6. How many complete groups? (whole number)

17. 6,300 ÷ 100 = ?

18. 2,958 ÷ 6 = ?

19. 88 ÷ 8 = ?

20. 56 people need taxis (4 per taxi). How many taxis needed?

🏆 Challenge — 8 Questions

1. 5,832 ÷ 8 = ?

2. A number divided by 7 gives 84 remainder 5. What is the original number?

3. 256 students going on a trip. Buses hold 48 passengers. How many buses are needed?

4. What is the smallest number greater than 1,000 that is divisible by both 3 and 5?

5. A farmer packs 6,847 apples into bags of 8. How many complete bags does he fill?

6. Divide 7,200 by 9, then divide the result by 4. What is the final answer?

7. A number is divisible by 2, 3, 5, and 9. It is between 100 and 200. What is it?

8. 4,316 ÷ 7 = ? (whole number quotient)