Find the odd number from the following options. 36, 64, 54, 108.

Introduction / Context:
This is an odd-one-out question involving four numbers: 36, 64, 54 and 108. You must identify which number does not share a common numerical property with the others. Such questions commonly use divisibility, parity, or special patterns (like squares or cubes) as the underlying rule.

Given Data / Assumptions:
- Numbers: 36, 64, 54, 108.
- Exactly one number behaves differently according to a simple numerical property.
- Common tests include divisibility by particular integers or recognition as a special kind of number.

Concept / Approach:
One convenient approach is to test divisibility by a shared factor. Looking at 36, 54 and 108, you may notice they are all multiples of 18. Checking 64 against this pattern quickly reveals that it does not fit. Another possible property is that 64 is a perfect power of 2 (2^6), while the others are not, but the simplest and most consistent pattern here is the “multiple of 18” test.

Step-by-Step Solution:
Step 1: Test 36 for divisibility by 18. 36 ÷ 18 = 2, so 36 is a multiple of 18. Step 2: Test 54 for divisibility by 18. 54 ÷ 18 = 3, so 54 is a multiple of 18. Step 3: Test 108 for divisibility by 18. 108 ÷ 18 = 6, so 108 is also a multiple of 18. Step 4: Test 64 for divisibility by 18. 64 ÷ 18 is not an integer (18 × 3 = 54, 18 × 4 = 72), so 64 is not divisible by 18. Step 5: Therefore, three numbers share the property “multiple of 18”, while 64 does not. This makes 64 the odd one out.

Verification / Alternative check:
Check other simple properties: parity and divisibility by 2 or 3. All four numbers are even. 36, 54 and 108 are all divisible by 9 as well, whereas 64 is not. So another way to see the pattern is that three of the numbers are divisible by 9 and 18, but 64 is not. Both viewpoints support the same conclusion that 64 stands apart from the rest.

Why Other Options Are Wrong:
- 36: divisible by 18 and 9, like 54 and 108.
- 54: divisible by 18 and 9, matching the common pattern.
- 108: also divisible by 18 and 9, fitting the same group property.

Common Pitfalls:
Some students might be distracted by the fact that 64 is a perfect square (8^2) and a power of 2, and assume that makes it the pattern, not the exception. However, the more consistent and natural property across the other three numbers is divisibility by 18 (and 9). Always look for a property shared by three numbers and missing in one, not the other way around.

Final Answer:
The odd number is 64, because it is not a multiple of 18 (or 9) while 36, 54 and 108 all are.