Classification (number properties): Three numbers are <em>not</em> perfect numbers; one number is a perfect number (equal to the sum of its proper divisors). Identify the odd one out.

Difficulty: Medium

Correct Answer: 28

Explanation:


Introduction / Context:
Number-property classification often focuses on special categories such as primes, squares, and perfect numbers. A perfect number equals the sum of its proper divisors (divisors less than the number itself). Among the options, 28 is the classic small perfect number; the others are not perfect. Recognizing perfect numbers is a standard competitive-exam micro-fact that can quickly unlock such items.



Given Data / Assumptions:

  • 12 → proper divisors: 1, 2, 3, 4, 6 (sum = 16 ≠ 12).
  • 28 → proper divisors: 1, 2, 4, 7, 14 (sum = 28 → perfect).
  • 52 → proper divisors: 1, 2, 4, 13, 26 (sum = 46 ≠ 52).
  • 96 → proper divisors sum is much larger than 96 (abundant), but not equal to 96.


Concept / Approach:
Compute the sum of proper divisors or recall the well-known early perfect numbers (6, 28, 496, 8128). If exactly one option matches, it is the outlier by property. This method exploits memorized landmarks to avoid time-consuming divisor calculations in the exam setting.



Step-by-Step Solution:

Recall perfect numbers list: 6, 28, 496, 8128...Check provided options against this list or verify by summing divisors.28 fits; others do not.


Verification / Alternative check:
Explicitly sum divisors for 28 as shown to confirm equality.



Why Other Options Are Wrong:

12, 52, 96 are not perfect; they are either abundant or deficient.


Common Pitfalls:
Confusing abundant numbers with perfect ones due to large divisor sums; equality is required.



Final Answer:
28

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