Prime and Composite Numbers Worksheets - 15 Worksheets Library - Free Printable

To solve the problem of identifying whether each number is prime or composite, we need to understand the definitions:

- Prime Number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
- Composite Number: A number greater than 1 that has more than two distinct positive divisors.

Step-by-Step Solution:

We will analyze each number from the list and determine if it is prime or composite. Here is the breakdown:

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#### Numbers 1–15:
1. 11: Prime (divisors are 1 and 11)
2. 12: Composite (divisors are 1, 2, 3, 4, 6, 12)
3. 15: Composite (divisors are 1, 3, 5, 15)
4. 13: Prime (divisors are 1 and 13)
5. 23: Prime (divisors are 1 and 23)
6. 25: Composite (divisors are 1, 5, 25)
7. 27: Composite (divisors are 1, 3, 9, 27)
8. 29: Prime (divisors are 1 and 29)
9. 31: Prime (divisors are 1 and 31)
10. 32: Composite (divisors are 1, 2, 4, 8, 16, 32)
11. 34: Composite (divisors are 1, 2, 17, 34)
12. 35: Composite (divisors are 1, 5, 7, 35)
13. 40: Composite (divisors are 1, 2, 4, 5, 8, 10, 20, 40)
14. 42: Composite (divisors are 1, 2, 3, 6, 7, 14, 21, 42)
15. 49: Composite (divisors are 1, 7, 49)

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#### Numbers 16–30:
16. 51: Composite (divisors are 1, 3, 17, 51)
17. 55: Composite (divisors are 1, 5, 11, 55)
18. 57: Composite (divisors are 1, 3, 19, 57)
19. 60: Composite (divisors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
20. 61: Prime (divisors are 1 and 61)
21. 67: Prime (divisors are 1 and 67)
22. 70: Composite (divisors are 1, 2, 5, 7, 10, 14, 35, 70)
23. 73: Prime (divisors are 1 and 73)
24. 75: Composite (divisors are 1, 3, 5, 15, 25, 75)
25. 77: Composite (divisors are 1, 7, 11, 77)
26. 81: Composite (divisors are 1, 3, 9, 27, 81)
27. 83: Prime (divisors are 1 and 83)
28. 87: Composite (divisors are 1, 3, 29, 87)
29. 89: Prime (divisors are 1 and 89)
30. 90: Composite (divisors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90)

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Final Answer:

Here is the completed worksheet with the classification of each number:

| Number | Classification |
|--------|----------------|
| 11 | Prime |
| 12 | Composite |
| 15 | Composite |
| 13 | Prime |
| 23 | Prime |
| 25 | Composite |
| 27 | Composite |
| 29 | Prime |
| 31 | Prime |
| 32 | Composite |
| 34 | Composite |
| 35 | Composite |
| 40 | Composite |
| 42 | Composite |
| 49 | Composite |
| 51 | Composite |
| 55 | Composite |
| 57 | Composite |
| 60 | Composite |
| 61 | Prime |
| 67 | Prime |
| 70 | Composite |
| 73 | Prime |
| 75 | Composite |
| 77 | Composite |
| 81 | Composite |
| 83 | Prime |
| 87 | Composite |
| 89 | Prime |
| 90 | Composite |

Thus, the final answer is:

\boxed{
\begin{array}{|c|c|}
\hline
\text{Number} & \text{Classification} \\
\hline
11 & \text{Prime} \\
12 & \text{Composite} \\
15 & \text{Composite} \\
13 & \text{Prime} \\
23 & \text{Prime} \\
25 & \text{Composite} \\
27 & \text{Composite} \\
29 & \text{Prime} \\
31 & \text{Prime} \\
32 & \text{Composite} \\
34 & \text{Composite} \\
35 & \text{Composite} \\
40 & \text{Composite} \\
42 & \text{Composite} \\
49 & \text{Composite} \\
51 & \text{Composite} \\
55 & \text{Composite} \\
57 & \text{Composite} \\
60 & \text{Composite} \\
61 & \text{Prime} \\
67 & \text{Prime} \\
70 & \text{Composite} \\
73 & \text{Prime} \\
75 & \text{Composite} \\
77 & \text{Composite} \\
81 & \text{Composite} \\
83 & \text{Prime} \\
87 & \text{Composite} \\
89 & \text{Prime} \\
90 & \text{Composite} \\
\hline
\end{array}
}