Classification – Odd one out (powers of two): Identify the number that does not belong: 56, 2, 128, 16.

Introduction / Context:A classic numeric classification is to check whether items are all powers of a base (most commonly 2 or 3). Here, three numbers are powers of 2; one is not. This yields an immediate 3-to-1 split.

Given Data / Assumptions:

• Candidates: 56, 2, 128, 16.
• We use the definition 2^k with integer k ≥ 0.

Concept / Approach:List nearby powers of 2 and compare: 2^1 = 2, 2^4 = 16, 2^7 = 128. Check 56 against this set. If one is not of the form 2^k, it is the outlier.

Step-by-Step Solution:2 is 2^1 → power of two.16 is 2^4 → power of two.128 is 2^7 → power of two.56 = 7 * 8 = 7 * 2^3, not a pure power of two.

Verification / Alternative check:Prime factorization confirms: 56 = 2^3 * 7 (extra prime 7), while genuine powers of two have only the prime factor 2. Therefore, 56 uniquely fails the criterion.

Why Other Options Are Wrong:

• 2, 16, 128 are clean powers of two (2^1, 2^4, 2^7).

Common Pitfalls:Equating multiples of powers of two with exact powers of two. Multiples introduce additional prime factors and break the definition.

Final Answer:56