Divisibility rules 4, 8, 11 and 12 worksheet - Free Printable

Let's solve this step by step using divisibility rules for the numbers 4, 8, 12, and 11.

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🔹 Divisibility Rules:

#### ✔ Divisible by 4:
- A number is divisible by 4 if the last two digits form a number divisible by 4.

#### ✔ Divisible by 8:
- A number is divisible by 8 if the last three digits form a number divisible by 8.

#### ✔ Divisible by 12:
- A number is divisible by 12 if it is divisible by both 3 and 4.
- For 3: Sum of digits divisible by 3.
- For 4: Last two digits divisible by 4.

#### ✔ Divisible by 11:
- A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is divisible by 11 (including 0).

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Now, let’s check each number one by one.

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🔹 1. 3896

#### ➤ Divisible by 4?
- Last two digits: 96
- 96 ÷ 4 = 24 → YES
✔ YES

#### ➤ Divisible by 8?
- Last three digits: 896
- 896 ÷ 8 = 112 → YES
✔ YES

#### ➤ Divisible by 12?
- Check divisibility by 3 and 4.
- Sum of digits: 3 + 8 + 9 + 6 = 26
- 26 is not divisible by 3 → ✘ Not divisible by 3
✘ NO

#### ➤ Divisible by 11?
- Positions:
- Odd positions (1st, 3rd): 3, 9 → sum = 12
- Even positions (2nd, 4th): 8, 6 → sum = 14
- Difference: |12 - 14| = 2 → not divisible by 11
✘ NO

> ✔ 3896 → YES, YES, NO, NO

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🔹 2. 4672

#### ➤ Divisible by 4?
- Last two digits: 72
- 72 ÷ 4 = 18 → YES
✔ YES

#### ➤ Divisible by 8?
- Last three digits: 672
- 672 ÷ 8 = 84 → YES
✔ YES

#### ➤ Divisible by 12?
- Check divisibility by 3 and 4.
- Sum of digits: 4 + 6 + 7 + 2 = 19
- 19 is not divisible by 3 → ✘
✘ NO

#### ➤ Divisible by 11?
- Positions:
- Odd: 4, 7 → sum = 11
- Even: 6, 2 → sum = 8
- Difference: |11 - 8| = 3 → not divisible by 11
✘ NO

> ✔ 4672 → YES, YES, NO, NO

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🔹 3. 7656

#### ➤ Divisible by 4?
- Last two digits: 56
- 56 ÷ 4 = 14 → YES
✔ YES

#### ➤ Divisible by 8?
- Last three digits: 656
- 656 ÷ 8 = 82 → YES
✔ YES

#### ➤ Divisible by 12?
- Check divisibility by 3 and 4.
- Sum of digits: 7 + 6 + 5 + 6 = 24
- 24 is divisible by 3 → ✔
- Already divisible by 4 → ✔
✔ YES

#### ➤ Divisible by 11?
- Positions:
- Odd: 7, 5 → sum = 12
- Even: 6, 6 → sum = 12
- Difference: |12 - 12| = 0 → divisible by 11
✔ YES

> ✔ 7656 → YES, YES, YES, YES

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🔹 4. 8888

#### ➤ Divisible by 4?
- Last two digits: 88
- 88 ÷ 4 = 22 → YES
✔ YES

#### ➤ Divisible by 8?
- Last three digits: 888
- 888 ÷ 8 = 111 → YES
✔ YES

#### ➤ Divisible by 12?
- Check 3 and 4.
- Sum of digits: 8 + 8 + 8 + 8 = 32
- 32 is not divisible by 3 → ✘
✘ NO

#### ➤ Divisible by 11?
- Positions:
- Odd: 8, 8 → sum = 16
- Even: 8, 8 → sum = 16
- Difference: |16 - 16| = 0 → divisible by 11
✔ YES

> ✔ 8888 → YES, YES, NO, YES

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🔹 5. 7326

#### ➤ Divisible by 4?
- Last two digits: 26
- 26 ÷ 4 = 6.5 → not divisible → ✘
✘ NO

#### ➤ Divisible by 8?
- Last three digits: 326
- 326 ÷ 8 = 40.75 → not divisible → ✘
✘ NO

#### ➤ Divisible by 12?
- Must be divisible by 3 and 4.
- Already not divisible by 4 → ✘
✘ NO

#### ➤ Divisible by 11?
- Positions:
- Odd: 7, 2 → sum = 9
- Even: 3, 6 → sum = 9
- Difference: |9 - 9| = 0 → divisible by 11
✔ YES

> ✔ 7326 → NO, NO, NO, YES

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✔ Final Answer Table:

| GIVEN | 4 | 8 | 12 | 11 |
|--------|-----|-----|-----|-----|
| 3896 | YES | YES | NO | NO |
| 4672 | YES | YES | NO | NO |
| 7656 | YES | YES | YES | YES |
| 8888 | YES | YES | NO | YES |
| 7326 | NO | NO | NO | YES |

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