Identifying the Odd Man Out
To determine the odd man out from the list of numbers 15, 21, 63, 81, and 69, we need to analyze their properties.
Step 1: Analyzing the Numbers
- 15:
- Prime factorization: 3 × 5
- Sum of digits: 1 + 5 = 6 (Even)
- 21:
- Prime factorization: 3 × 7
- Sum of digits: 2 + 1 = 3 (Odd)
- 63:
- Prime factorization: 3 × 3 × 7
- Sum of digits: 6 + 3 = 9 (Odd)
- 81:
- Prime factorization: 3 × 3 × 3 × 3
- Sum of digits: 8 + 1 = 9 (Odd)
- 69:
- Prime factorization: 3 × 23
- Sum of digits: 6 + 9 = 15 (Odd)
Step 2: Observing Patterns
- All numbers except 15 have an odd sum of digits.
- 15 stands out as it has an even sum of digits.
Conclusion
Based on the analysis, the odd man out is:
- 15
It is the only number with an even sum of digits, while all other numbers have an odd sum. Thus, 15 is the unique number that does not fit the pattern established by the other numbers in the group.