In the number series 8, 14, 24, 60 and 180, which one number is the odd man out because it does not follow the same simple divisibility pattern as the others?

Introduction / Context:
This problem asks you to identify the odd man out in a short numerical series. Such questions usually rely on a very simple number property such as divisibility, parity, or being a multiple of a fixed integer. Spotting these properties quickly is very useful in aptitude exams where speed matters.

Given Data / Assumptions:
The given terms of the series are:

• 8
• 14
• 24
• 60
• 180

Exactly one number is assumed to violate a clear divisibility pattern shared by the others.

Concept / Approach:
A quick way to attack an odd man out question is to check divisibility by small integers such as 2, 3, 4, 5, and so on. Here, all numbers are even, so we go one step further and test divisibility by 4, since many aptitude questions use this simple rule. The number that fails the shared property is the odd one out.

Step-by-Step Solution:
Step 1: Test divisibility by 4 using the standard rule. A number is divisible by 4 if the last two digits form a number divisible by 4.Step 2: Check 8. It is 4 * 2, so it is divisible by 4.Step 3: Check 24. It is 4 * 6, so it is divisible by 4.Step 4: Check 60. The last two digits 60 give 60 / 4 = 15, so 60 is divisible by 4.Step 5: Check 180. The last two digits 80 give 80 / 4 = 20, so 180 is also divisible by 4.Step 6: Check 14. The last two digits 14 give 14 / 4 = 3.5, which is not an integer, so 14 is not divisible by 4.

Verification / Alternative check:
We can factor each number to double check: 8 = 2^3, 24 = 2^3 * 3, 60 = 2^2 * 3 * 5, and 180 = 2^2 * 3^2 * 5, all of which contain at least two factors of 2 and so are multiples of 4. But 14 = 2 * 7 has only one factor 2, so it is not a multiple of 4. This confirms that 14 does not share the same divisibility property as the others.

Why Other Options Are Wrong:
180, 60 and 24 all share the property of being divisible by 4 as well as by 2. They fit naturally into a group of numbers that are multiples of 4. Removing any of them would leave 14 still standing out as non divisible by 4, so they cannot be considered the correct odd man out.

Common Pitfalls:
Candidates sometimes overthink such questions and search for complicated patterns involving multiplication or powers. In exam settings it is important to first check very simple properties like divisibility or parity. Once you notice that only 14 fails the divisibility by 4 test, the answer becomes straightforward.

Final Answer:
The number that does not share the common divisibility pattern is 14.