Composite vs. prime classification — pick the odd one out Set: 4, 6, 8, 9, 10, 11, 12. Which single number is different from the rest?

Introduction / Context:
Odd-man-out questions often hinge on a basic number-theory property: most elements share “composite” status while one is “prime.” Identifying primality quickly separates the outlier from the rest.

Given Data / Assumptions:

• Numbers provided: 4, 6, 8, 9, 10, 11, 12.
• We use the standard definition of prime and composite.

Concept / Approach:
Test each number: composite numbers have nontrivial factors; primes do not (other than 1 and itself). If exactly one number is prime and all others are composite, that prime is the odd one out.

Step-by-Step Solution:
4 = 2 * 2 ⇒ composite.6 = 2 * 3 ⇒ composite.8 = 2 * 2 * 2 ⇒ composite.9 = 3 * 3 ⇒ composite.10 = 2 * 5 ⇒ composite.12 = 3 * 4 ⇒ composite.11 has no divisors other than 1 and 11 ⇒ prime.

Verification / Alternative check:
Among the set, only 11 cannot be expressed as a product of smaller integers. Hence it differs from all others, which are composite.

Why Other Options Are Wrong:
4, 6, 8, 9, 10, and 12 are all composite. They share the majority property and thus are not the odd ones out.

Common Pitfalls:
Mistaking 9 as prime (it is 3 * 3), or overlooking that “even vs. odd” is not the core property here because 9 is odd yet composite. The prime/composite distinction is decisive.

Final Answer:
11