Divisibility Rule for 6 worksheet with numbers to test divisibility.

To determine whether a number is divisible by 6, we need to check two conditions based on the divisibility rules:

1. The number must be divisible by 2.
2. The number must be divisible by 3.

Divisibility Rule for 2:

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

Divisibility Rule for 3:

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

Steps to Solve:

For each number in the list, we will:
1. Check if the number is divisible by 2.
2. Check if the number is divisible by 3.
3. If both conditions are satisfied, the number is divisible by 6.

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Let's solve each number step-by-step:

#### 1) 4,728
- Divisibility by 2: Last digit is 8 (even). → Yes.
- Divisibility by 3: Sum of digits = \(4 + 7 + 2 + 8 = 21\). Since 21 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 2) 93
- Divisibility by 2: Last digit is 3 (odd). → No.
- Divisibility by 3: Sum of digits = \(9 + 3 = 12\). Since 12 is divisible by 3, → Yes.
- Conclusion: Not divisible by 6.

#### 3) 627
- Divisibility by 2: Last digit is 7 (odd). → No.
- Divisibility by 3: Sum of digits = \(6 + 2 + 7 = 15\). Since 15 is divisible by 3, → Yes.
- Conclusion: Not divisible by 6.

#### 4) 13,224
- Divisibility by 2: Last digit is 4 (even). → Yes.
- Divisibility by 3: Sum of digits = \(1 + 3 + 2 + 2 + 4 = 12\). Since 12 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 5) 72
- Divisibility by 2: Last digit is 2 (even). → Yes.
- Divisibility by 3: Sum of digits = \(7 + 2 = 9\). Since 9 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 6) 374
- Divisibility by 2: Last digit is 4 (even). → Yes.
- Divisibility by 3: Sum of digits = \(3 + 7 + 4 = 14\). Since 14 is not divisible by 3, → No.
- Conclusion: Not divisible by 6.

#### 7) 37,821
- Divisibility by 2: Last digit is 1 (odd). → No.
- Divisibility by 3: Sum of digits = \(3 + 7 + 8 + 2 + 1 = 21\). Since 21 is divisible by 3, → Yes.
- Conclusion: Not divisible by 6.

#### 8) 57,330
- Divisibility by 2: Last digit is 0 (even). → Yes.
- Divisibility by 3: Sum of digits = \(5 + 7 + 3 + 3 + 0 = 18\). Since 18 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 9) 5,844
- Divisibility by 2: Last digit is 4 (even). → Yes.
- Divisibility by 3: Sum of digits = \(5 + 8 + 4 + 4 = 21\). Since 21 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 10) 7,352
- Divisibility by 2: Last digit is 2 (even). → Yes.
- Divisibility by 3: Sum of digits = \(7 + 3 + 5 + 2 = 17\). Since 17 is not divisible by 3, → No.
- Conclusion: Not divisible by 6.

#### 11) 1,745
- Divisibility by 2: Last digit is 5 (odd). → No.
- Divisibility by 3: Sum of digits = \(1 + 7 + 4 + 5 = 17\). Since 17 is not divisible by 3, → No.
- Conclusion: Not divisible by 6.

#### 12) 82,356
- Divisibility by 2: Last digit is 6 (even). → Yes.
- Divisibility by 3: Sum of digits = \(8 + 2 + 3 + 5 + 6 = 24\). Since 24 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 13) 8,232
- Divisibility by 2: Last digit is 2 (even). → Yes.
- Divisibility by 3: Sum of digits = \(8 + 2 + 3 + 2 = 15\). Since 15 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 14) 6,360
- Divisibility by 2: Last digit is 0 (even). → Yes.
- Divisibility by 3: Sum of digits = \(6 + 3 + 6 + 0 = 15\). Since 15 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 15) 96,324
- Divisibility by 2: Last digit is 4 (even). → Yes.
- Divisibility by 3: Sum of digits = \(9 + 6 + 3 + 2 + 4 = 24\). Since 24 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

#### 16) 459
- Divisibility by 2: Last digit is 9 (odd). → No.
- Divisibility by 3: Sum of digits = \(4 + 5 + 9 = 18\). Since 18 is divisible by 3, → Yes.
- Conclusion: Not divisible by 6.

#### 17) 2,530
- Divisibility by 2: Last digit is 0 (even). → Yes.
- Divisibility by 3: Sum of digits = \(2 + 5 + 3 + 0 = 10\). Since 10 is not divisible by 3, → No.
- Conclusion: Not divisible by 6.

#### 18) 24
- Divisibility by 2: Last digit is 4 (even). → Yes.
- Divisibility by 3: Sum of digits = \(2 + 4 = 6\). Since 6 is divisible by 3, → Yes.
- Conclusion: Divisible by 6.

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Final Answers:

1. 4,728: Divisible by 6
2. 93: Not divisible by 6
3. 627: Not divisible by 6
4. 13,224: Divisible by 6
5. 72: Divisible by 6
6. 374: Not divisible by 6
7. 37,821: Not divisible by 6
8. 57,330: Divisible by 6
9. 5,844: Divisible by 6
10. 7,352: Not divisible by 6
11. 1,745: Not divisible by 6
12. 82,356: Divisible by 6
13. 8,232: Divisible by 6
14. 6,360: Divisible by 6
15. 96,324: Divisible by 6
16. 459: Not divisible by 6
17. 2,530: Not divisible by 6
18. 24: Divisible by 6

Boxed Answer:

\[
\boxed{
\begin{array}{ll}
1) & \text{Divisible by 6} \\
2) & \text{Not divisible by 6} \\
3) & \text{Not divisible by 6} \\
4) & \text{Divisible by 6} \\
5) & \text{Divisible by 6} \\
6) & \text{Not divisible by 6} \\
7) & \text{Not divisible by 6} \\
8) & \text{Divisible by 6} \\
9) & \text{Divisible by 6} \\
10) & \text{Not divisible by 6} \\
11) & \text{Not divisible by 6} \\
12) & \text{Divisible by 6} \\
13) & \text{Divisible by 6} \\
14) & \text{Divisible by 6} \\
15) & \text{Divisible by 6} \\
16) & \text{Not divisible by 6} \\
17) & \text{Not divisible by 6} \\
18) & \text{Divisible by 6} \\
\end{array}
}
\]