Question

Which are composite numbers
Explain why they are composite or prime
5, 17, 27, 29, and 31

Answer 1

To determine whether the given numbers (5, 17, 27, 29, and 31) are composite or prime, we first need to define what these terms mean:

- **Prime numbers** are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
- **Composite numbers** are natural numbers greater than 1 that have more than two positive divisors.

Now, let's analyze each number:

1. **5**:
- Divisors: 1, 5
- Since it has exactly two divisors (1 and itself), 5 is a **prime number**.

2. **17**:
- Divisors: 1, 17
- It also has exactly two divisors (1 and itself), so 17 is a **prime number**.

3. **27**:
- Divisors: 1, 3, 9, 27
- Since 27 can be divided by more than two numbers (1, 3, 9, and 27), it is a **composite number**.

4. **29**:
- Divisors: 1, 29
- It has exactly two divisors (1 and itself), making 29 a **prime number**.

5. **31**:
- Divisors: 1, 31
- With exactly two divisors (1 and itself), 31 is a **prime number**.

### Summary:
- **Composite Numbers**: 27
- **Prime Numbers**: 5, 17, 29, 31