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

Problem Overview:

The task involves identifying whether each given number is prime or composite by listing its factors. Additionally, you need to circle all the prime numbers in a provided list.

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Step-by-Step Solution:

#### Part 1: Determine Prime or Composite for Each Number
We will analyze each number (43, 45, 47, 53, 55) and determine if it is prime or composite by listing its factors.

1. Number: 43
- Factors: To find the factors of 43, we check divisibility by integers from 2 to √43 (approximately 6.5).
- 43 is not divisible by 2, 3, 4, 5, or 6.
- Therefore, the only factors are 1 and 43.
- Conclusion: Prime

2. Number: 45
- Factors: Check divisibility by integers from 2 to √45 (approximately 6.7).
- Divisible by 3 (45 ÷ 3 = 15), so factors include 1, 3, 5, 9, 15, and 45.
- Conclusion: Composite

3. Number: 47
- Factors: Check divisibility by integers from 2 to √47 (approximately 6.8).
- 47 is not divisible by 2, 3, 4, 5, or 6.
- Therefore, the only factors are 1 and 47.
- Conclusion: Prime

4. Number: 53
- Factors: Check divisibility by integers from 2 to √53 (approximately 7.3).
- 53 is not divisible by 2, 3, 4, 5, 6, or 7.
- Therefore, the only factors are 1 and 53.
- Conclusion: Prime

5. Number: 55
- Factors: Check divisibility by integers from 2 to √55 (approximately 7.4).
- Divisible by 5 (55 ÷ 5 = 11), so factors include 1, 5, 11, and 55.
- Conclusion: Composite

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#### Part 2: Circle All Prime Numbers in the Given List
The list of numbers is:
```
23 31 76 55 77
25 56 47 23 80 71
37 73 51 12 89 95
```

We will identify which of these numbers are prime by checking their factors.

1. 23: Only factors are 1 and 23. Prime
2. 31: Only factors are 1 and 31. Prime
3. 76: Divisible by 2, 4, 19, etc. Composite
4. 55: Divisible by 5 and 11. Composite
5. 77: Divisible by 7 and 11. Composite
6. 25: Divisible by 5. Composite
7. 56: Divisible by 2, 4, 7, etc. Composite
8. 47: Only factors are 1 and 47. Prime
9. 23: Already identified as prime. Prime
10. 80: Divisible by 2, 4, 5, etc. Composite
11. 71: Only factors are 1 and 71. Prime
12. 37: Only factors are 1 and 37. Prime
13. 73: Only factors are 1 and 73. Prime
14. 51: Divisible by 3 and 17. Composite
15. 12: Divisible by 2, 3, 4, 6. Composite
16. 89: Only factors are 1 and 89. Prime
17. 95: Divisible by 5 and 19. Composite

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Final Answer:

#### Part 1: Prime or Composite for Each Number
1. 43: Prime
2. 45: Composite
3. 47: Prime
4. 53: Prime
5. 55: Composite

#### Part 2: Circle All Prime Numbers
The prime numbers in the list are:
```
23, 31, 47, 23, 71, 37, 73, 89
```

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Boxed Final Answer:

$$
\boxed{
\text{Part 1: } \text{43 (Prime), 45 (Composite), 47 (Prime), 53 (Prime), 55 (Composite)} \\
\text{Part 2: } \text{Circle: 23, 31, 47, 23, 71, 37, 73, 89}
}
$$