To find all the prime and composite numbers between 30 and 40, we will follow these steps:
### Step 1: Understand the definitions
- **Prime Numbers**: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. This means it can only be divided evenly (without a remainder) by 1 and the number itself.
- **Composite Numbers**: A composite number is a number greater than 1 that has more than two positive divisors. This means it can be divided evenly by numbers other than 1 and itself.
### Step 2: List the numbers between 30 and 40
The numbers between 30 and 40 are:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40.
### Step 3: Identify prime numbers
Now, we will check each number to see if it is prime:
- **30**: Divisible by 1, 2, 3, 5, 6, 10, 15, 30 (Composite)
- **31**: Divisible only by 1 and 31 (Prime)
- **32**: Divisible by 1, 2, 4, 8, 16, 32 (Composite)
- **33**: Divisible by 1, 3, 11, 33 (Composite)
- **34**: Divisible by 1, 2, 17, 34 (Composite)
- **35**: Divisible by 1, 5, 7, 35 (Composite)
- **36**: Divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36 (Composite)
- **37**: Divisible only by 1 and 37 (Prime)
- **38**: Divisible by 1, 2, 19, 38 (Composite)
- **39**: Divisible by 1, 3, 13, 39 (Composite)
- **40**: Divisible by 1, 2, 4, 5, 8, 10, 20, 40 (Composite)
### Step 4: List the prime and composite numbers
From our checks:
- **Prime Numbers**: 31, 37
- **Composite Numbers**: 30, 32, 33, 34, 35, 36, 38, 39, 40
### Final Answer
- **Prime Numbers between 30 and 40**: 31, 37
- **Composite Numbers between 30 and 40**: 30, 32, 33, 34, 35, 36, 38, 39, 40
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