Classification – Odd one out (pure powers of 2) In the list below, three numbers are exact powers of 2. Identify the one that is not a pure power of 2 and mark it as the odd one out.

Introduction / Context:
Number classification often distinguishes exact powers from composites that include extra factors. Here, the theme is powers of 2. Recognizing the pattern 2, 4, 8, 16, 32, 64, 128, … helps you isolate the mismatch quickly.

Given Data / Assumptions:

• Options: 2, 16, 56, 128
• Power-of-2 sequence is strictly 2^k for integer k ≥ 1.

Concept / Approach:
Check whether each number can be written as 2^k. If an extra prime factor beyond 2 appears, the number is not a pure power of 2.

Step-by-Step Solution:
2 = 2^1 → power of 2.16 = 2^4 → power of 2.128 = 2^7 → power of 2.56 = 2^3 * 7 → not a pure power of 2.

Verification / Alternative check:
Binary perspective: powers of 2 have exactly one 1-bit in binary. 56 in binary is 111000 (three 1-bits), hence not a power of 2.

Why Other Options Are Wrong:

• 2: Exact power of 2.
• 16: Exact power of 2.
• 128: Exact power of 2.
• None of these: There is a clear odd one (56).

Common Pitfalls:
Confusing “even” with “power of 2.” Many even numbers are not pure powers because they include other prime factors (like 7 in 56).

Final Answer:
56