Classification – Multiples of 12: pick the odd one out. Three numbers are exact multiples of 12; one is not divisible by 12. Which number is different? Options: 52, 96, 24, 36.

Introduction / Context:
Divisibility and common multiples underpin many number classifications. Testing for a shared divisor quickly reveals the exception.

Given Data / Assumptions:

• 12 = 3 * 4 = 2^2 * 3.
• Check each option for divisibility by 12.

Concept / Approach:
A number is divisible by 12 if it is divisible by both 3 and 4. Use quick tests (sum of digits for 3; last two digits for 4).

Step-by-Step Solution:
96: divisible by 3 (9+6=15) and by 4 (last two digits 96 → 24*4) → multiple.24: 24=12*2 → multiple.36: divisible by 3 (3+6=9) and by 4 (36=9*4) → multiple.52: 5+2=7 (not divisible by 3); although 52 is divisible by 4, it fails the 3 test → not a multiple of 12.

Verification / Alternative check:
Prime factors: 52=2^2*13 lacks factor 3; others include both 2^2 and 3.

Why Other Options Are Wrong:
96/24/36: Each is an exact multiple of 12 and belongs together.

Common Pitfalls:
Assuming evenness implies divisibility by 12; it does not without the factor 3.

Final Answer:
52