Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Let's solve each part of this worksheet step by step. We'll use the divisibility rules for 3, 6, and 9.

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🔹 Divisibility Rules:

- Divisible by 3: The sum of the digits is divisible by 3.
- Divisible by 6: Must be divisible by both 2 and 3.
- Divisible by 2 → last digit is even (0, 2, 4, 6, 8).
- Divisible by 3 → sum of digits divisible by 3.
- Divisible by 9: The sum of the digits is divisible by 9.

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## ✔ Problem 1: Circle numbers divisible by 3

We check each number: sum the digits and see if divisible by 3.

| Number | Sum of Digits | Divisible by 3? |
|--------|----------------|------------------|
| 1,128 | 1+1+2+8 = 12 → 12÷3=4 ✔️ | ✔ |
| 2,101 | 2+1+0+1 = 4 ✘ | ✘ |
| 2,235 | 2+2+3+5 = 12 ✔️ | ✔ |
| 3,122 | 3+1+2+2 = 8 ✘ | ✘ |
| 4,445 | 4+4+4+5 = 17 ✘ | ✘ |
| 2,088 | 2+0+8+8 = 18 ✔️ | ✔ |
| 9,457 | 9+4+5+7 = 25 ✘ | ✘ |
| 5,004 | 5+0+0+4 = 9 ✔️ | ✔ |
| 6,625 | 6+6+2+5 = 19 ✘ | ✘ |
| 7,134 | 7+1+3+4 = 15 ✔️ | ✔ |
| 9,120 | 9+1+2+0 = 12 ✔️ | ✔ |
| 5,228 | 5+2+2+8 = 17 ✘ | ✘ |
| 4,002 | 4+0+0+2 = 6 ✔️ | ✔ |
| 1,124 | 1+1+2+4 = 8 ✘ | ✘ |
| 7,886 | 7+8+8+6 = 29 ✘ | ✘ |
| 9,999 | 9+9+9+9 = 36 ✔️ | ✔ |
| 1,750 | 1+7+5+0 = 13 ✘ | ✘ |
| 5,661 | 5+6+6+1 = 18 ✔️ | ✔ |

✔ Numbers divisible by 3:
1,128, 2,235, 2,088, 5,004, 7,134, 9,120, 4,002, 9,999, 5,661

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## ✔ Problem 2: Circle numbers divisible by 6

Must be divisible by both 2 and 3.

Check each number:

| Number | Ends in even? | Sum of digits | Div by 3? | Div by 6? |
|--------|---------------|----------------|------------|-----------|
| 7,500 | Yes (0) | 7+5+0+0 = 12 ✔️ | ✔ | ✔ |
| 9,567 | No (7 odd) | 9+5+6+7 = 27 ✔️ | ✔ | ✘ |
| 9,072 | Yes (2) | 9+0+7+2 = 18 ✔️ | ✔ | ✔ |
| 2,199 | No (9 odd) | 2+1+9+9 = 21 ✔️ | ✔ | ✘ |
| 6,864 | Yes (4) | 6+8+6+4 = 24 ✔️ | ✔ | ✔ |
| 5,400 | Yes (0) | 5+4+0+0 = 9 ✔️ | ✔ | ✔ |
| 5,290 | Yes (0) | 5+2+9+0 = 16 ✘ | ✘ | ✘ |
| 7,398 | Yes (8) | 7+3+9+8 = 27 ✔️ | ✔ | ✔ |
| 6,092 | Yes (2) | 6+0+9+2 = 17 ✘ | ✘ | ✘ |
| 9,666 | Yes (6) | 9+6+6+6 = 27 ✔️ | ✔ | ✔ |
| 8,862 | Yes (2) | 8+8+6+2 = 24 ✔️ | ✔ | ✔ |
| 3,125 | No (5 odd) | 3+1+2+5 = 11 ✘ | ✘ | ✘ |
| 6,834 | Yes (4) | 6+8+3+4 = 21 ✔️ | ✔ | ✔ |
| 2,907 | No (7 odd) | 2+9+0+7 = 18 ✔️ | ✔ | ✘ |
| 5,335 | No (5 odd) | 5+3+3+5 = 16 ✘ | ✘ | ✘ |
| 7,421 | No (1 odd) | 7+4+2+1 = 14 ✘ | ✘ | ✘ |
| 3,444 | Yes (4) | 3+4+4+4 = 15 ✔️ | ✔ | ✔ |
| 7,728 | Yes (8) | 7+7+2+8 = 24 ✔️ | ✔ | ✔ |

✔ Numbers divisible by 6:
7,500, 9,072, 6,864, 5,400, 7,398, 9,666, 8,862, 6,834, 3,444, 7,728

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## ✔ Problem 3: Circle numbers divisible by 9

Sum of digits must be divisible by 9.

| Number | Sum of Digits | Div by 9? |
|--------|----------------|----------|
| 9,099 | 9+0+9+9 = 27 ✔️ | ✔ |
| 1,145 | 1+1+4+5 = 11 ✘ | ✘ |
| 8,089 | 8+0+8+9 = 25 ✘ | ✘ |
| 6,228 | 6+2+2+8 = 18 ✔️ | ✔ |
| 9,139 | 9+1+3+9 = 22 ✘ | ✘ |
| 4,950 | 4+9+5+0 = 18 ✔️ | ✔ |
| 6,192 | 6+1+9+2 = 18 ✔️ | ✔ |
| 4,383 | 4+3+8+3 = 18 ✔️ | ✔ |
| 4,188 | 4+1+8+8 = 21 ✘ | ✘ |
| 1,099 | 1+0+9+9 = 19 ✘ | ✘ |
| 7,144 | 7+1+4+4 = 16 ✘ | ✘ |
| 1,926 | 1+9+2+6 = 18 ✔️ | ✔ |
| 8,865 | 8+8+6+5 = 27 ✔️ | ✔ |
| 9,455 | 9+4+5+5 = 23 ✘ | ✘ |
| 3,322 | 3+3+2+2 = 10 ✘ | ✘ |
| 2,997 | 2+9+9+7 = 27 ✔️ | ✔ |
| 1,035 | 1+0+3+5 = 9 ✔️ | ✔ |
| 1,494 | 1+4+9+4 = 18 ✔️ | ✔ |

✔ Numbers divisible by 9:
9,099, 6,228, 4,950, 6,192, 4,383, 1,926, 8,865, 2,997, 1,035, 1,494

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✔ Final Answers:

#### 1. Divisible by 3:
1,128, 2,235, 2,088, 5,004, 7,134, 9,120, 4,002, 9,999, 5,661

#### 2. Divisible by 6:
7,500, 9,072, 6,864, 5,400, 7,398, 9,666, 8,862, 6,834, 3,444, 7,728

#### 3. Divisible by 9:
9,099, 6,228, 4,950, 6,192, 4,383, 1,926, 8,865, 2,997, 1,035, 1,494

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