Write all the prime numbers and composite numbers between:
70 and 80

Answer

To find all the prime and composite numbers between 70 and 80, we will first define what prime and composite numbers are, and then identify the numbers in the specified range.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Prime Numbers**: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, it has exactly two distinct positive divisors: 1 and itself.
- **Composite Numbers**: A composite number is a natural number greater than 1 that is not prime. This means it has more than two positive divisors.

2. **List the Numbers Between 70 and 80**:
- The numbers we need to consider are: 71, 72, 73, 74, 75, 76, 77, 78, 79.

3. **Identify Prime and Composite Numbers**:
- **70**: Composite (divisible by 1, 2, 5, 7, 10, 14, 35, 70)
- **71**: Prime (only divisible by 1 and 71)
- **72**: Composite (divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72)
- **73**: Prime (only divisible by 1 and 73)
- **74**: Composite (divisible by 1, 2, 37, 74)
- **75**: Composite (divisible by 1, 3, 5, 15, 25, 75)
- **76**: Composite (divisible by 1, 2, 4, 19, 38, 76)
- **77**: Composite (divisible by 1, 7, 11, 77)
- **78**: Composite (divisible by 1, 2, 3, 6, 13, 26, 39, 78)
- **79**: Prime (only divisible by 1 and 79)
- **80**: Composite (divisible by 1, 2, 4, 5, 8, 10, 16, 20, 40, 80)

4. **Compile the Results**:
- **Prime Numbers**: 71, 73, 79
- **Composite Numbers**: 70, 72, 74, 75, 76, 77, 78, 80

### Final Answer:
- **Prime Numbers between 70 and 80**: 71, 73, 79
- **Composite Numbers between 70 and 80**: 70, 72, 74, 75, 76, 77, 78, 80