Divisibility Rules worksheet with exercises and answers for numbers divisible by 2, 3, 4, 5, 6, and 9.

To solve the problem, we will apply the divisibility rules provided in the worksheet to each number. Let's go through each section step by step.

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Divisibility by 2

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

1. 56: Last digit is 6 → Yes
2. 101: Last digit is 1 → No
3. 250: Last digit is 0 → Yes
4. 3,077: Last digit is 7 → No
5. 22,098: Last digit is 8 → Yes

Answers:
- 56: Yes
- 101: No
- 250: Yes
- 3,077: No
- 22,098: Yes

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Divisibility by 3

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

1. 66: Sum of digits = 6 + 6 = 12 → 12 is divisible by 3 → Yes
2. 113: Sum of digits = 1 + 1 + 3 = 5 → 5 is not divisible by 3 → No
3. 255: Sum of digits = 2 + 5 + 5 = 12 → 12 is divisible by 3 → Yes
4. 3,078: Sum of digits = 3 + 0 + 7 + 8 = 18 → 18 is divisible by 3 → Yes
5. 10,125: Sum of digits = 1 + 0 + 1 + 2 + 5 = 9 → 9 is divisible by 3 → Yes

Answers:
- 66: Yes
- 113: No
- 255: Yes
- 3,078: Yes
- 10,125: Yes

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Divisibility by 4

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

1. 82: Last two digits are 82 → 82 ÷ 4 = 20.5 (not an integer) → No
2. 116: Last two digits are 16 → 16 ÷ 4 = 4 (integer) → Yes
3. 114: Last two digits are 14 → 14 ÷ 4 = 3.5 (not an integer) → No
4. 3,072: Last two digits are 72 → 72 ÷ 4 = 18 (integer) → Yes
5. 16,164: Last two digits are 64 → 64 ÷ 4 = 16 (integer) → Yes

Answers:
- 82: No
- 116: Yes
- 114: No
- 3,072: Yes
- 16,164: Yes

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Divisibility by 5

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

1. 74: Last digit is 4 → No
2. 125: Last digit is 5 → Yes
3. 280: Last digit is 0 → Yes
4. 1,090: Last digit is 0 → Yes
5. 24,013: Last digit is 3 → No

Answers:
- 74: No
- 125: Yes
- 280: Yes
- 1,090: Yes
- 24,013: No

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Divisibility by 6

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

1. 72: Divisible by 2 (last digit is 2) and divisible by 3 (sum of digits = 7 + 2 = 9, which is divisible by 3) → Yes
2. 112: Divisible by 2 (last digit is 2) but not divisible by 3 (sum of digits = 1 + 1 + 2 = 4, which is not divisible by 3) → No
3. 246: Divisible by 2 (last digit is 6) and divisible by 3 (sum of digits = 2 + 4 + 6 = 12, which is divisible by 3) → Yes
4. 2,208: Divisible by 2 (last digit is 8) and divisible by 3 (sum of digits = 2 + 2 + 0 + 8 = 12, which is divisible by 3) → Yes
5. 17,333: Not divisible by 2 (last digit is 3) → No

Answers:
- 72: Yes
- 112: No
- 246: Yes
- 2,208: Yes
- 17,333: No

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Divisibility by 9

A number is divisible by 9 if the sum of its digits is a multiple of 9.

1. 89: Sum of digits = 8 + 9 = 17 → 17 is not divisible by 9 → No
2. 117: Sum of digits = 1 + 1 + 7 = 9 → 9 is divisible by 9 → Yes
3. 414: Sum of digits = 4 + 1 + 4 = 9 → 9 is divisible by 9 → Yes
4. 6,021: Sum of digits = 6 + 0 + 2 + 1 = 9 → 9 is divisible by 9 → Yes
5. 99,899: Sum of digits = 9 + 9 + 8 + 9 + 9 = 44 → 44 is not divisible by 9 → No

Answers:
- 89: No
- 117: Yes
- 414: Yes
- 6,021: Yes
- 99,899: No

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Final Answer

Combining all the results:

| Divisible by 2? | Divisible by 3? | Divisible by 4? | Divisible by 5? | Divisible by 6? | Divisible by 9? |
|------------------|------------------|------------------|------------------|------------------|------------------|
| 56: Yes | 66: Yes | 82: No | 74: No | 72: Yes | 89: No |
| 101: No | 113: No | 116: Yes | 125: Yes | 112: No | 117: Yes |
| 250: Yes | 255: Yes | 114: No | 280: Yes | 246: Yes | 414: Yes |
| 3,077: No | 3,078: Yes | 3,072: Yes | 1,090: Yes | 2,208: Yes | 6,021: Yes |
| 22,098: Yes | 10,125: Yes | 16,164: Yes | 24,013: No | 17,333: No | 99,899: No |

Boxed Final Answer:
\[
\boxed{
\begin{array}{c|c|c|c|c|c}
\text{Divisible by 2?} & \text{Divisible by 3?} & \text{Divisible by 4?} & \text{Divisible by 5?} & \text{Divisible by 6?} & \text{Divisible by 9?} \\
\hline
56: \text{Yes} & 66: \text{Yes} & 82: \text{No} & 74: \text{No} & 72: \text{Yes} & 89: \text{No} \\
101: \text{No} & 113: \text{No} & 116: \text{Yes} & 125: \text{Yes} & 112: \text{No} & 117: \text{Yes} \\
250: \text{Yes} & 255: \text{Yes} & 114: \text{No} & 280: \text{Yes} & 246: \text{Yes} & 414: \text{Yes} \\
3,077: \text{No} & 3,078: \text{Yes} & 3,072: \text{Yes} & 1,090: \text{Yes} & 2,208: \text{Yes} & 6,021: \text{Yes} \\
22,098: \text{Yes} & 10,125: \text{Yes} & 16,164: \text{Yes} & 24,013: \text{No} & 17,333: \text{No} & 99,899: \text{No} \\
\end{array}
}
\]