Answer key for a prime and composite numbers worksheet, showing solutions to questions with a playful cartoon illustration.

It looks like you've uploaded an image of a worksheet titled "Prime and Composite" with an answer key. The task involves identifying whether given numbers are prime or composite, based on their factors.

Let me go through the problems and explain the solutions step by step, using the logic behind prime and composite numbers.

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🔹 Definitions:

- A prime number is a number greater than 1 that has only two factors: 1 and itself.
- A composite number has more than two factors.
- Note: 1 is neither prime nor composite.

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✔ Problem 1:

> "List all the factors for these numbers:
> a) 2 → 1, 2
> b) 4 → 1, 2, 4
> c) 6 → 1, 2, 3, 6"

Then it asks:
> "Is 2 prime or composite?" → prime
> "Is 4 prime or composite?" → composite
> "Is 6 prime or composite?" → composite

✔ Explanation:
- 2 has only two factors (1 and 2) → prime
- 4 has three factors (1, 2, 4) → composite
- 6 has four factors (1, 2, 3, 6) → composite

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✔ Problem 2:

> "List all the factors for these numbers:
> a) 8 → 1, 2, 4, 8
> b) 9 → 1, 3, 9
> c) 10 → 1, 2, 5, 10"

Then:
> "Is 8 prime or composite?" → composite
> "Is 9 prime or composite?" → composite
> "Is 10 prime or composite?" → composite

✔ Explanation:
- 8: more than two factors → composite
- 9: factors are 1, 3, 9 → composite (3×3)
- 10: 1, 2, 5, 10 → composite

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✔ Problem 3:

> "List all the factors for these numbers:
> a) 11 → 1, 11
> b) 12 → 1, 2, 3, 4, 6, 12
> c) 13 → 1, 13"

Then:
> "Is 11 prime or composite?" → prime
> "Is 12 prime or composite?" → composite
> "Is 13 prime or composite?" → prime

✔ Explanation:
- 11: only divisible by 1 and 11 → prime
- 12: many factors → composite
- 13: only divisible by 1 and 13 → prime

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✔ Problem 4:

> "List all the factors for these numbers:
> a) 17 → 1, 17
> b) 18 → 1, 2, 3, 6, 9, 18
> c) 19 → 1, 19"

Then:
> "Is 17 prime or composite?" → prime
> "Is 18 prime or composite?" → composite
> "Is 19 prime or composite?" → prime

✔ Explanation:
- 17 and 19 are both prime (only divisible by 1 and themselves)
- 18 has multiple factors → composite

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✔ Problem 5:

> "List all the factors for these numbers:
> a) 20 → 1, 2, 4, 5, 10, 20
> b) 21 → 1, 3, 7, 21
> c) 22 → 1, 2, 11, 22"

Then:
> "Is 20 prime or composite?" → composite
> "Is 21 prime or composite?" → composite
> "Is 22 prime or composite?" → composite

✔ Explanation:
All three have more than two factors → composite

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✔ Final Summary Table:

| Number | Factors | Prime or Composite |
|--------|----------------------------|---------------------|
| 2 | 1, 2 | Prime |
| 4 | 1, 2, 4 | Composite |
| 6 | 1, 2, 3, 6 | Composite |
| 8 | 1, 2, 4, 8 | Composite |
| 9 | 1, 3, 9 | Composite |
| 10 | 1, 2, 5, 10 | Composite |
| 11 | 1, 11 | Prime |
| 12 | 1, 2, 3, 4, 6, 12 | Composite |
| 13 | 1, 13 | Prime |
| 17 | 1, 17 | Prime |
| 18 | 1, 2, 3, 6, 9, 18 | Composite |
| 19 | 1, 19 | Prime |
| 20 | 1, 2, 4, 5, 10, 20 | Composite |
| 21 | 1, 3, 7, 21 | Composite |
| 22 | 1, 2, 11, 22 | Composite |

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📌 Key Takeaway:

To determine if a number is prime or composite, list its factors. If it has only two factors (1 and itself), it's prime. If it has more than two, it's composite.

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