Short Answer 
The analysis categorizes numbers into even and odd, lists their factors, and distinguishes between prime and composite numbers. The prime number identified as an outlier is 3, as it has only two divisors, unlike the others.
Step 1: Analyze Odd and Even Numbers
Begin by categorizing the numbers into even and odd groups. This will help identify patterns based on their parity. The classifications are as follows:
- Even Numbers: 12, 24, 300
- Odd Numbers: 9, 3, 39
Step 2: Determine Factors of Each Number
Next, investigate the factors of each number to understand their divisibility. Factors are crucial for this analysis, as they reveal the structure of each number. Below is the list of factors for each number:
- 12: 1, 2, 3, 4, 6, 12
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 9: 1, 3, 9
- 3: 1, 3
- 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 60, 75, 100, 150, 300
- 39: 1, 3, 13, 39
Step 3: Identify Prime and Composite Numbers
Finally, classify each number as prime or composite. This classification is key to finding the outlier. In this case:
- Composite Numbers: 12, 24, 300, 9, 39
- Prime Number: 3
From this analysis, it is evident that the only number that does not share the same pattern is 3, as it is a prime number with only two divisors.