Classification – Odd one out (prime vs composite) Among the following integers, three are prime while exactly one is composite. Identify the composite number and mark it as the odd one out.

Introduction / Context:
Prime recognition is a core classification skill. Test-makers frequently present three unmistakable primes along with a composite that yields to a small-prime divisibility check. Spotting the composite quickly is the key to speed.

Given Data / Assumptions:

• Candidates: 53, 67, 73, 87
• We separate primes from composites using small divisibility tests.

Concept / Approach:
Check divisibility by 2, 3, 5 first, then 7 and 11 as needed. The digit-sum rule is especially useful for screening multiples of 3.

Step-by-Step Solution:
87 → 8 + 7 = 15 → divisible by 3 → composite (3 * 29).53 → not divisible by 2, 3, 5, 7 → prime.67 → not divisible by 2, 3, 5, 7 → prime.73 → not divisible by 2, 3, 5, 7 → prime.

Verification / Alternative check:
Trial division up to sqrt(87) < 10 confirms 87 has factor 3. The others have no small prime divisors within their square-root bounds.

Why Other Options Are Wrong:

• 53: Prime, so not the odd composite.
• 67: Prime, so not the odd composite.
• 73: Prime, so not the odd composite.
• None of these: There is a single composite (87).

Common Pitfalls:
Confusing “odd” with “prime.” Many odd numbers are composite; always apply check rules.

Final Answer:
87