Answer key for prime and composite numbers worksheet.

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

Let me explain the solution and how to interpret this answer key.

---

🔍 What is Prime and Composite?

- 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 (i.e., it can be divided evenly by numbers other than 1 and itself).
- The number 1 is neither prime nor composite.

---

📋 Answer Key Breakdown

Here’s the table from your image, explained:

| Number | Factors | Prime or Composite |
|--------|---------|--------------------|
| 10 | 1, 2, 5, and 10 | Composite |
| 5 | 1 and 5 | Prime |
| 12 | 1, 2, 3, 4, 6, and 12 | Composite |
| 18 | 1, 2, 3, 6, 9, and 18 | Composite |
| 41 | 1 and 41 | Prime |
| 15 | 1, 3, 5, and 15 | Composite |
| 2 | 1 and 2 | Prime |
| 49 | 1, 7, and 49 | Composite |
| 73 | 1 and 73 | Prime |
| 33 | 1, 3, 11, and 33 | Composite |
| 21 | 1, 3, 7, and 21 | Composite |

---

✔ Explanation of Each Entry

1. 10 → Factors: 1, 2, 5, 10 → More than two factors → Composite
2. 5 → Only 1 and 5 → Prime
3. 12 → Many factors (1, 2, 3, 4, 6, 12) → Composite
4. 18 → Factors include 1, 2, 3, 6, 9, 18 → Composite
5. 41 → Only divisible by 1 and 41 → Prime
6. 15 → 1, 3, 5, 15 → Composite
7. 2 → Smallest prime number → Prime
8. 49 → 1, 7, 49 → 7×7 = 49 → Composite
9. 73 → Only 1 and 73 → Prime
10. 33 → 1, 3, 11, 33 → 3×11 = 33 → Composite
11. 21 → 1, 3, 7, 21 → 3×7 = 21 → Composite

---

💡 Tips for Solving Such Problems

- Start by checking divisibility:
- Even numbers (except 2) are composite.
- Numbers ending in 5 or 0 (except 5) are divisible by 5 → composite.
- Try dividing by small primes: 2, 3, 5, 7, etc.
- If no divisors found other than 1 and the number itself → Prime.

---

✔ Summary

This answer key correctly identifies each number as prime or composite based on its factors. It's a great tool for learning how to classify numbers.

If you need help solving similar problems or want to practice more, let me know!