Divisibility Rule for 6 Worksheets - Free Printable

To determine whether a number is divisible by 6, we use the divisibility rule for 6:

> A number is divisible by 6 if and only if it is divisible by both 2 and 3.

🔹 Divisibility Rules:

- Divisible by 2: The number must be even (last digit is 0, 2, 4, 6, or 8).
- Divisible by 3: The sum of the digits must be divisible by 3.

Let’s apply this rule to each number in your list.

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✔ Step-by-step Analysis:

#### 1) 4,728
- Last digit: 8 → even → divisible by 2 ✔
- Sum of digits: 4 + 7 + 2 + 8 = 21 → 21 ÷ 3 = 7 → divisible by 3 ✔
→ Yes

#### 2) 93
- Last digit: 3 → odd → not divisible by 2 ✘
→ No

#### 3) 627
- Last digit: 7 → odd → not divisible by 2 ✘
→ No

#### 4) 13,224
- Last digit: 4 → even → divisible by 2 ✔
- Sum: 1 + 3 + 2 + 2 + 4 = 12 → 12 ÷ 3 = 4 → divisible by 3 ✔
→ Yes

#### 5) 72
- Last digit: 2 → even → divisible by 2 ✔
- Sum: 7 + 2 = 9 → divisible by 3 ✔
→ Yes

#### 6) 374
- Last digit: 4 → even → divisible by 2 ✔
- Sum: 3 + 7 + 4 = 14 → 14 ÷ 3 = 4.66… → not divisible by 3 ✘
→ No

#### 7) 37,821
- Last digit: 1 → odd → not divisible by 2 ✘
→ No

#### 8) 57,330
- Last digit: 0 → even → divisible by 2 ✔
- Sum: 5 + 7 + 3 + 3 + 0 = 18 → divisible by 3 ✔
→ Yes

#### 9) 5,844
- Last digit: 4 → even → divisible by 2 ✔
- Sum: 5 + 8 + 4 + 4 = 21 → divisible by 3 ✔
→ Yes

#### 10) 7,352
- Last digit: 2 → even → divisible by 2 ✔
- Sum: 7 + 3 + 5 + 2 = 17 → 17 ÷ 3 = 5.66… → not divisible by 3 ✘
→ No

#### 11) 1,745
- Last digit: 5 → odd → not divisible by 2 ✘
→ No

#### 12) 82,356
- Last digit: 6 → even → divisible by 2 ✔
- Sum: 8 + 2 + 3 + 5 + 6 = 24 → divisible by 3 ✔
→ Yes

#### 13) 8,232
- Last digit: 2 → even → divisible by 2 ✔
- Sum: 8 + 2 + 3 + 2 = 15 → divisible by 3 ✔
→ Yes

#### 14) 6,360
- Last digit: 0 → even → divisible by 2 ✔
- Sum: 6 + 3 + 6 + 0 = 15 → divisible by 3 ✔
→ Yes

#### 15) 96,324
- Last digit: 4 → even → divisible by 2 ✔
- Sum: 9 + 6 + 3 + 2 + 4 = 24 → divisible by 3 ✔
→ Yes

#### 16) 459
- Last digit: 9 → odd → not divisible by 2 ✘
→ No

#### 17) 2,530
- Last digit: 0 → even → divisible by 2 ✔
- Sum: 2 + 5 + 3 + 0 = 10 → 10 ÷ 3 = 3.33… → not divisible by 3 ✘
→ No

#### 18) 24
- Last digit: 4 → even → divisible by 2 ✔
- Sum: 2 + 4 = 6 → divisible by 3 ✔
→ Yes

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✔ Final Answers:

1) Yes
2) No
3) No
4) Yes
5) Yes
6) No
7) No
8) Yes
9) Yes
10) No
11) No
12) Yes
13) Yes
14) Yes
15) Yes
16) No
17) No
18) Yes

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✔ Summary: A number is divisible by 6 only if it passes both the divisibility tests for 2 and 3. Always check both conditions!