  What is an interesting number theoretic or a combinatorial characterization
of the divisors of 24 amongst all positive integers? In this paper I will
provide one characterization in terms of modular multiplication tables. This
idea evolved interestingly from a question raised by a student in my elementary
number theory class. I will give the characterization and then provide 5 proofs
using various techniques: Chinese remainder theorem, structure theory of units,
Dirichlet's theorem on primes in an arithmetic progression, Bertrand-Chebyshev
theorem, and results of Erdos and Ramanujan on the pi(x) function.
