Classification – Odd one out (divisibility by 16) Among the following integers, exactly three are divisible by 16 without remainder. Identify the number that is NOT divisible by 16 and mark it as the odd one out.

Introduction / Context:
Odd-one-out questions often test a single property shared by most options while exactly one violates it. Here, the property is divisibility by a fixed integer (16). Recognizing factors and applying quick divisibility checks help you eliminate distractors efficiently.

Given Data / Assumptions:

• Numbers given: 272, 210, 240, 304
• Target property: divisibility by 16
• All are positive integers; no hidden conditions

Concept / Approach:
For any integer n, n is divisible by 16 if n / 16 is an integer with remainder 0. Because 16 = 2^4, another way is to check whether the number has at least four factors of 2 (i.e., divisible by 2, 4, 8, and 16). Mental division or factorization works well here.

Step-by-Step Solution:
Check 272: 272 / 16 = 17 → integer → divisible by 16.Check 240: 240 / 16 = 15 → integer → divisible by 16.Check 304: 304 / 16 = 19 → integer → divisible by 16.Check 210: 210 / 16 = 13.125 → not an integer → NOT divisible by 16.

Verification / Alternative check:
Prime-factor viewpoint: 272 = 16 * 17 has 2^4; 240 = 16 * 15 has 2^4; 304 = 16 * 19 has 2^4. Meanwhile, 210 = 2 * 3 * 5 * 7 has only one factor of 2, far short of 2^4, confirming it is not divisible by 16.

Why Other Options Are Wrong:

• 272: Exactly divisible by 16.
• 240: Exactly divisible by 16.
• 304: Exactly divisible by 16.
• None of these: There is a clear odd one out (210), so this is incorrect.

Common Pitfalls:
Candidates sometimes test only divisibility by 2 or 4 and stop early; being even or divisible by 4 does not guarantee divisibility by 16. Always confirm through division by 16 or ensure four factors of 2 are present.

Final Answer:
210