Prime and Composite Numbers Worksheet for students to complete.

I will solve this problem by completing the table for each number, identifying its factors and determining whether it is prime or composite.

Let me start by examining the first row, which serves as an example. The number 25 has factors 1, 5, and 25, and it is labeled as "Composite". This makes sense because a composite number has more than two distinct positive divisors (factors), while a prime number has exactly two: 1 and itself.

I'll now work through each remaining number in the table one by one to find its factors and classify it as prime or composite.

For 36:
- Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Since it has more than two factors, it is Composite.

For 43:
- Factors: 1, 43
- It only has two factors, so it is Prime.

For 47:
- Factors: 1, 47
- It only has two factors, so it is Prime.

For 51:
- Factors: 1, 3, 17, 51
- Since it has more than two factors, it is Composite.

For 55:
- Factors: 1, 5, 11, 55
- Since it has more than two factors, it is Composite.

For 59:
- Factors: 1, 59
- It only has two factors, so it is Prime.

For 60:
- Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Since it has more than two factors, it is Composite.

For 61:
- Factors: 1, 61
- It only has two factors, so it is Prime.

Now I will present the completed table.

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Completed Table:

| Number | Factors | Prime or Composite |
|--------|--------------------------|--------------------|
| 25 | 1, 5, 25 | Composite |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | Composite |
| 43 | 1, 43 | Prime |
| 47 | 1, 47 | Prime |
| 51 | 1, 3, 17, 51 | Composite |
| 55 | 1, 5, 11, 55 | Composite |
| 59 | 1, 59 | Prime |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | Composite |
| 61 | 1, 61 | Prime |

This completes the task. Each number has been analyzed for its factors, and correctly classified as either prime or composite based on the definition that a prime number has exactly two distinct positive divisors (1 and itself), while a composite number has more than two.