Divisibility Rule worksheet for practicing identifying numbers divisible by 2, 3, 4, and 5.

To solve the problem, we need to apply the divisibility rules for the numbers 2, 3, 4, and 5. Let's go through each section step by step.

---

Divisibility Rule for 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

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

#### Solution:
- 1024: Last digit is 4 (even) → Divisible by 2
- 3265: Last digit is 5 (odd) → Not divisible by 2
- 364: Last digit is 4 (even) → Divisible by 2
- 2482: Last digit is 2 (even) → Divisible by 2
- 908: Last digit is 8 (even) → Divisible by 2
- 147: Last digit is 7 (odd) → Not divisible by 2
- 108: Last digit is 8 (even) → Divisible by 2
- 1478: Last digit is 8 (even) → Divisible by 2
- 272: Last digit is 2 (even) → Divisible by 2
- 18: Last digit is 8 (even) → Divisible by 2
- 27: Last digit is 7 (odd) → Not divisible by 2
- 326: Last digit is 6 (even) → Divisible by 2
- 59: Last digit is 9 (odd) → Not divisible by 2
- 102: Last digit is 2 (even) → Divisible by 2
- 4824: Last digit is 4 (even) → Divisible by 2
- 362: Last digit is 2 (even) → Divisible by 2
- 54: Last digit is 4 (even) → Divisible by 2
- 242: Last digit is 2 (even) → Divisible by 2
- 125: Last digit is 5 (odd) → Not divisible by 2
- 248: Last digit is 8 (even) → Divisible by 2
- 3102: Last digit is 2 (even) → Divisible by 2
- 124: Last digit is 4 (even) → Divisible by 2
- 163: Last digit is 3 (odd) → Not divisible by 2
- 1093: Last digit is 3 (odd) → Not divisible by 2

Circled numbers:
```
1024, 364, 2482, 908, 108, 1478, 272, 18, 326, 102, 4824, 362, 54, 242, 248, 3102, 124
```

---

Divisibility Rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

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

#### Solution:
- 1236: Sum of digits = 1 + 2 + 3 + 6 = 12 (divisible by 3) → Divisible by 3
- 2406: Sum of digits = 2 + 4 + 0 + 6 = 12 (divisible by 3) → Divisible by 3
- 5312: Sum of digits = 5 + 3 + 1 + 2 = 11 (not divisible by 3) → Not divisible by 3
- 54: Sum of digits = 5 + 4 = 9 (divisible by 3) → Divisible by 3
- 5431: Sum of digits = 5 + 4 + 3 + 1 = 13 (not divisible by 3) → Not divisible by 3
- 1024: Sum of digits = 1 + 0 + 2 + 4 = 7 (not divisible by 3) → Not divisible by 3
- 1083: Sum of digits = 1 + 0 + 8 + 3 = 12 (divisible by 3) → Divisible by 3
- 109: Sum of digits = 1 + 0 + 9 = 10 (not divisible by 3) → Not divisible by 3
- 4725: Sum of digits = 4 + 7 + 2 + 5 = 18 (divisible by 3) → Divisible by 3
- 309: Sum of digits = 3 + 0 + 9 = 12 (divisible by 3) → Divisible by 3
- 2475: Sum of digits = 2 + 4 + 7 + 5 = 18 (divisible by 3) → Divisible by 3
- 789: Sum of digits = 7 + 8 + 9 = 24 (divisible by 3) → Divisible by 3
- 58: Sum of digits = 5 + 8 = 13 (not divisible by 3) → Not divisible by 3
- 2475: Already checked → Divisible by 3
- 1029: Sum of digits = 1 + 0 + 2 + 9 = 12 (divisible by 3) → Divisible by 3
- 1243: Sum of digits = 1 + 2 + 4 + 3 = 10 (not divisible by 3) → Not divisible by 3
- 1096: Sum of digits = 1 + 0 + 9 + 6 = 16 (not divisible by 3) → Not divisible by 3
- 632: Sum of digits = 6 + 3 + 2 = 11 (not divisible by 3) → Not divisible by 3
- 105: Sum of digits = 1 + 0 + 5 = 6 (divisible by 3) → Divisible by 3
- 4782: Sum of digits = 4 + 7 + 8 + 2 = 21 (divisible by 3) → Divisible by 3
- 2403: Sum of digits = 2 + 4 + 0 + 3 = 9 (divisible by 3) → Divisible by 3
- 983: Sum of digits = 9 + 8 + 3 = 20 (not divisible by 3) → Not divisible by 3
- 3124: Sum of digits = 3 + 1 + 2 + 4 = 10 (not divisible by 3) → Not divisible by 3
- 8701: Sum of digits = 8 + 7 + 0 + 1 = 16 (not divisible by 3) → Not divisible by 3

Circled numbers:
```
1236, 2406, 54, 1083, 4725, 309, 2475, 789, 1029, 105, 4782, 2403
```

---

Divisibility Rule for 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

#### Numbers to check:
```
2048, 108, 3254, 1436, 2489, 548
96, 512, 1368, 2478, 3690, 5458
2785, 6330, 3580, 196, 312, 84
4720, 1236, 2740, 3648, 5488, 3624
```

#### Solution:
- 2048: Last two digits = 48 (divisible by 4) → Divisible by 4
- 108: Last two digits = 08 (divisible by 4) → Divisible by 4
- 3254: Last two digits = 54 (not divisible by 4) → Not divisible by 4
- 1436: Last two digits = 36 (divisible by 4) → Divisible by 4
- 2489: Last two digits = 89 (not divisible by 4) → Not divisible by 4
- 548: Last two digits = 48 (divisible by 4) → Divisible by 4
- 96: Last two digits = 96 (divisible by 4) → Divisible by 4
- 512: Last two digits = 12 (divisible by 4) → Divisible by 4
- 1368: Last two digits = 68 (divisible by 4) → Divisible by 4
- 2478: Last two digits = 78 (not divisible by 4) → Not divisible by 4
- 3690: Last two digits = 90 (not divisible by 4) → Not divisible by 4
- 5458: Last two digits = 58 (not divisible by 4) → Not divisible by 4
- 2785: Last two digits = 85 (not divisible by 4) → Not divisible by 4
- 6330: Last two digits = 30 (not divisible by 4) → Not divisible by 4
- 3580: Last two digits = 80 (divisible by 4) → Divisible by 4
- 196: Last two digits = 96 (divisible by 4) → Divisible by 4
- 312: Last two digits = 12 (divisible by 4) → Divisible by 4
- 84: Last two digits = 84 (divisible by 4) → Divisible by 4
- 4720: Last two digits = 20 (divisible by 4) → Divisible by 4
- 1236: Last two digits = 36 (divisible by 4) → Divisible by 4
- 2740: Last two digits = 40 (divisible by 4) → Divisible by 4
- 3648: Last two digits = 48 (divisible by 4) → Divisible by 4
- 5488: Last two digits = 88 (divisible by 4) → Divisible by 4
- 3624: Last two digits = 24 (divisible by 4) → Divisible by 4

Circled numbers:
```
2048, 108, 1436, 548, 96, 512, 1368, 3580, 196, 312, 84, 4720, 1236, 2740, 3648, 5488, 3624
```

---

Divisibility Rule for 5

A number is divisible by 5 if its last digit is 0 or 5.

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

#### Solution:
- 105: Last digit is 5 → Divisible by 5
- 2485: Last digit is 5 → Divisible by 5
- 120: Last digit is 0 → Divisible by 5
- 3654: Last digit is 4 → Not divisible by 5
- 148: Last digit is 8 → Not divisible by 5
- 369: Last digit is 9 → Not divisible by 5
- 1485: Last digit is 5 → Divisible by 5
- 2475: Last digit is 5 → Divisible by 5
- 203: Last digit is 3 → Not divisible by 5
- 470: Last digit is 0 → Divisible by 5
- 3475: Last digit is 5 → Divisible by 5
- 620: Last digit is 0 → Divisible by 5
- 95: Last digit is 5 → Divisible by 5
- 780: Last digit is 0 → Divisible by 5
- 4731: Last digit is 1 → Not divisible by 5
- 5745: Last digit is 5 → Divisible by 5
- 4284: Last digit is 4 → Not divisible by 5
- 325: Last digit is 5 → Divisible by 5
- 985: Last digit is 5 → Divisible by 5
- 2539: Last digit is 9 → Not divisible by 5
- 1250: Last digit is 0 → Divisible by 5
- 4725: Last digit is 5 → Divisible by 5
- 3525: Last digit is 5 → Divisible by 5
- 6251: Last digit is 1 → Not divisible by 5

Circled numbers:
```
105, 2485, 120, 1485, 2475, 470, 3475, 620, 95, 780, 5745, 325, 985, 1250, 4725, 3525
```

---

Final Answer

```
\boxed{
\text{Divisible by 2: } 1024, 364, 2482, 908, 108, 1478, 272, 18, 326, 102, 4824, 362, 54, 242, 248, 3102, 124 \\
\text{Divisible by 3: } 1236, 2406, 54, 1083, 4725, 309, 2475, 789, 1029, 105, 4782, 2403 \\
\text{Divisible by 4: } 2048, 108, 1436, 548, 96, 512, 1368, 3580, 196, 312, 84, 4720, 1236, 2740, 3648, 5488, 3624 \\
\text{Divisible by 5: } 105, 2485, 120, 1485, 2475, 470, 3475, 620, 95, 780, 5745, 325, 985, 1250, 4725, 3525
}
```