Choose the odd number: Among 78, 48, 72, and 54, exactly one number has 13 as a prime factor. Identify that distinct number.

Introduction / Context:
Several classification items rely on a specific hidden factor. Here, we test for the presence of the prime 13 in the factorization.

Given Data / Assumptions:

• Numbers: 78, 48, 72, 54.
• Check prime factor 13.

Concept / Approach:
Factor each number or check divisibility by 13. Because 13 * 6 = 78, this quickly singles out the outlier.

Step-by-Step Solution:

Verification / Alternative check:
Dividing each by 13: only 78/13 = 6 is integer; others are not.

Why Other Options Are Wrong:
48, 72, and 54 share small prime factors 2 and 3 but lack 13.

Common Pitfalls:
Using only parity or sum-of-digits rules; those do not detect the presence of 13.

Final Answer:
78 is the only number with prime factor 13 and is the odd number.