Divisibility Rules Worksheets - 15 Worksheets Library - Free Printable

Let's solve the Divisibility Rule worksheet step by step. The goal is to circle numbers divisible by 2, 3, 4, and 5, based on the divisibility rules.

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🔢 Divisibility Rules Reminder:

- Divisible by 2: Number ends in an even digit (0, 2, 4, 6, 8).
- Divisible by 3: Sum of digits is divisible by 3.
- Divisible by 4: Last two digits form a number divisible by 4.
- Divisible by 5: Ends in 0 or 5.

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We'll go through each section one by one.

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## ✔ Section 1: Circle numbers divisible by 2

Rule: Ends in even digit (0, 2, 4, 6, 8)

List:
```
1024 3265 364 2482 908 147
108 1478 272 18 27 326
59 102 4824 362 54 242
125 248 3102 124 163 1093
```

Now check each:

- 1024 → ends in 4 → ✔
- 3265 → ends in 5 → ✘
- 364 → ends in 4 → ✔
- 2482 → ends in 2 → ✔
- 908 → ends in 8 → ✔
- 147 → ends in 7 → ✘
- 108 → ends in 8 → ✔
- 1478 → ends in 8 → ✔
- 272 → ends in 2 → ✔
- 18 → ends in 8 → ✔
- 27 → ends in 7 → ✘
- 326 → ends in 6 → ✔
- 59 → ends in 9 → ✘
- 102 → ends in 2 → ✔
- 4824 → ends in 4 → ✔
- 362 → ends in 2 → ✔
- 54 → ends in 4 → ✔
- 242 → ends in 2 → ✔
- 125 → ends in 5 → ✘
- 248 → ends in 8 → ✔
- 3102 → ends in 2 → ✔
- 124 → ends in 4 → ✔
- 163 → ends in 3 → ✘
- 1093 → ends in 3 → ✘

✔ Numbers divisible by 2:
> 1024, 364, 2482, 908, 108, 1478, 272, 18, 326, 102, 4824, 362, 54, 242, 248, 3102, 124

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## ✔ Section 2: Circle numbers divisible by 3

Rule: Sum of digits divisible by 3

List:
```
1236 2406 5312 54 5431 1024
1083 109 4725 309 2475 789
58 2475 1029 1243 1096 632
105 4782 2403 983 3124 8701
```

Check each:

1. 1236: 1+2+3+6 = 12 → 12÷3=4 → ✔
2. 2406: 2+4+0+6 = 12 → ✔
3. 5312: 5+3+1+2 = 11 → ✘
4. 54: 5+4 = 9 → ✔
5. 5431: 5+4+3+1 = 13 → ✘
6. 1024: 1+0+2+4 = 7 → ✘
7. 1083: 1+0+8+3 = 12 → ✔
8. 109: 1+0+9 = 10 → ✘
9. 4725: 4+7+2+5 = 18 → ✔
10. 309: 3+0+9 = 12 → ✔
11. 2475: 2+4+7+5 = 18 → ✔
12. 789: 7+8+9 = 24 → ✔
13. 58: 5+8 = 13 → ✘
14. 2475: already done → ✔
15. 1029: 1+0+2+9 = 12 → ✔
16. 1243: 1+2+4+3 = 10 → ✘
17. 1096: 1+0+9+6 = 16 → ✘
18. 632: 6+3+2 = 11 → ✘
19. 105: 1+0+5 = 6 → ✔
20. 4782: 4+7+8+2 = 21 → ✔
21. 2403: 2+4+0+3 = 9 → ✔
22. 983: 9+8+3 = 20 → ✘
23. 3124: 3+1+2+4 = 10 → ✘
24. 8701: 8+7+0+1 = 16 → ✘

✔ Numbers divisible by 3:
> 1236, 2406, 54, 1083, 4725, 309, 2475, 789, 2475 (duplicate), 1029, 105, 4782, 2403

Note: 2475 appears twice — circle both instances.

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## ✔ Section 3: Circle numbers divisible by 4

Rule: Last two digits form a number divisible by 4

List:
```
2048 108 3254 1436 2489 548
96 512 1368 2478 3690 4584
2785 6330 3580 196 312 84
4720 1236 2740 3648 5488 3624
```

Check last two digits:

1. 2048 → 48 ÷ 4 = 12 → ✔
2. 108 → 08 = 8 → 8÷4=2 → ✔
3. 3254 → 54 ÷ 4 = 13.5 → ✘
4. 1436 → 36 ÷ 4 = 9 → ✔
5. 2489 → 89 ÷ 4 = 22.25 → ✘
6. 548 → 48 ÷ 4 = 12 → ✔
7. 96 → 96 ÷ 4 = 24 → ✔
8. 512 → 12 ÷ 4 = 3 → ✔
9. 1368 → 68 ÷ 4 = 17 → ✔
10. 2478 → 78 ÷ 4 = 19.5 → ✘
11. 3690 → 90 ÷ 4 = 22.5 → ✘
12. 4584 → 84 ÷ 4 = 21 → ✔
13. 2785 → 85 ÷ 4 = 21.25 → ✘
14. 6330 → 30 ÷ 4 = 7.5 → ✘
15. 3580 → 80 ÷ 4 = 20 → ✔
16. 196 → 96 ÷ 4 = 24 → ✔
17. 312 → 12 ÷ 4 = 3 → ✔
18. 84 → 84 ÷ 4 = 21 → ✔
19. 4720 → 20 ÷ 4 = 5 → ✔
20. 1236 → 36 ÷ 4 = 9 → ✔
21. 2740 → 40 ÷ 4 = 10 → ✔
22. 3648 → 48 ÷ 4 = 12 → ✔
23. 5488 → 88 ÷ 4 = 22 → ✔
24. 3624 → 24 ÷ 4 = 6 → ✔

✔ Numbers divisible by 4:
> 2048, 108, 1436, 548, 96, 512, 1368, 4584, 3580, 196, 312, 84, 4720, 1236, 2740, 3648, 5488, 3624

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## ✔ Section 4: Circle numbers divisible by 5

Rule: Ends in 0 or 5

List:
```
105 2485 120 3654 148 369
1485 2475 203 470 3475 620
95 780 4731 5745 4284 325
985 2539 1250 4725 3525 6251
```

Check last digit:

1. 105 → ends in 5 → ✔
2. 2485 → ends in 5 → ✔
3. 120 → ends in 0 → ✔
4. 3654 → ends in 4 → ✘
5. 148 → ends in 8 → ✘
6. 369 → ends in 9 → ✘
7. 1485 → ends in 5 → ✔
8. 2475 → ends in 5 → ✔
9. 203 → ends in 3 → ✘
10. 470 → ends in 0 → ✔
11. 3475 → ends in 5 → ✔
12. 620 → ends in 0 → ✔
13. 95 → ends in 5 → ✔
14. 780 → ends in 0 → ✔
15. 4731 → ends in 1 → ✘
16. 5745 → ends in 5 → ✔
17. 4284 → ends in 4 → ✘
18. 325 → ends in 5 → ✔
19. 985 → ends in 5 → ✔
20. 2539 → ends in 9 → ✘
21. 1250 → ends in 0 → ✔
22. 4725 → ends in 5 → ✔
23. 3525 → ends in 5 → ✔
24. 6251 → ends in 1 → ✘

✔ Numbers divisible by 5:
> 105, 2485, 120, 1485, 2475, 470, 3475, 620, 95, 780, 5745, 325, 985, 1250, 4725, 3525

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✔ Final Answer Summary:

#### 🟦 Divisible by 2:
> 1024, 364, 2482, 908, 108, 1478, 272, 18, 326, 102, 4824, 362, 54, 242, 248, 3102, 124

#### 🟨 Divisible by 3:
> 1236, 2406, 54, 1083, 4725, 309, 2475, 789, 1029, 105, 4782, 2403

(2475 appears twice — both should be circled)

#### 🟩 Divisible by 4:
> 2048, 108, 1436, 548, 96, 512, 1368, 4584, 3580, 196, 312, 84, 4720, 1236, 2740, 3648, 5488, 3624

#### 🟪 Divisible by 5:
> 105, 2485, 120, 1485, 2475, 470, 3475, 620, 95, 780, 5745, 325, 985, 1250, 4725, 3525

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💡 Tip for students: Use these rules to quickly check without dividing! Practice helps memorize patterns.

Let me know if you'd like this as a printable answer key!