Christmas Math 5th Grade Worksheets - Free Printable

Problem Analysis:

The task involves identifying whether given numbers are prime or composite. Let's break it down step by step:

#### 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.

#### Steps to Solve:
1. Check if a number is prime or composite:
- For each number, determine its divisors.
- If the number has only two divisors (1 and itself), it is prime.
- If the number has more than two divisors, it is composite.

2. Apply the definition to each number in the worksheet.

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Solution:

#### Part a: Tell if 9 is a prime or a composite number.
- Divisors of 9: 1, 3, 9
- Since 9 has more than two divisors (1, 3, 9), it is composite.

#### Part b: Tell if 17 is a prime or a composite number.
- Divisors of 17: 1, 17
- Since 17 has exactly two divisors (1 and 17), it is prime.

#### Part c: Say if the following numbers are prime or composite.
We will analyze each number one by one:

1. 33:
- Divisors: 1, 3, 11, 33
- More than two divisors → Composite

2. 59:
- Divisors: 1, 59
- Exactly two divisors → Prime

3. 83:
- Divisors: 1, 83
- Exactly two divisors → Prime

4. 53:
- Divisors: 1, 53
- Exactly two divisors → Prime

5. 100:
- Divisors: 1, 2, 4, 5, 10, 20, 25, 50, 100
- More than two divisors → Composite

6. 49:
- Divisors: 1, 7, 49
- More than two divisors → Composite

7. 81:
- Divisors: 1, 3, 9, 27, 81
- More than two divisors → Composite

8. 67:
- Divisors: 1, 67
- Exactly two divisors → Prime

9. 94:
- Divisors: 1, 2, 47, 94
- More than two divisors → Composite

10. 79:
- Divisors: 1, 79
- Exactly two divisors → Prime

11. 71:
- Divisors: 1, 71
- Exactly two divisors → Prime

12. 61:
- Divisors: 1, 61
- Exactly two divisors → Prime

13. 43:
- Divisors: 1, 43
- Exactly two divisors → Prime

14. 0:
- By definition, 0 is neither prime nor composite.

15. 70:
- Divisors: 1, 2, 5, 7, 10, 14, 35, 70
- More than two divisors → Composite

16. 71:
- Divisors: 1, 71
- Exactly two divisors → Prime

17. 2:
- Divisors: 1, 2
- Exactly two divisors → Prime

18. 10:
- Divisors: 1, 2, 5, 10
- More than two divisors → Composite

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Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{a. } 9 & \text{Composite} \\
\text{b. } 17 & \text{Prime} \\
\text{c. } & \begin{array}{ccc}
33 & \text{Composite} & 59 & \text{Prime} & 83 & \text{Prime} \\
53 & \text{Prime} & 100 & \text{Composite} & 49 & \text{Composite} \\
81 & \text{Composite} & 67 & \text{Prime} & 94 & \text{Composite} \\
79 & \text{Prime} & 71 & \text{Prime} & 61 & \text{Prime} \\
43 & \text{Prime} & 0 & \text{Neither} & 70 & \text{Composite} \\
71 & \text{Prime} & 2 & \text{Prime} & 10 & \text{Composite} \\
\end{array}
\end{array}
}
\]