Well, 120 is multiply-perfect, superabundant, highly composite, a triangular, tetrahedral, and hexagonal number, the sum of a twin prime pair, the sum of four consecutive primes, four consecutive powers of two, four consecutive powers of three, and so on. It's the lowest number to have 16 factors, so the factors thing I've got down.

In what I'm working on there are precisely 12 months in a year, and so 120 months = 1 decade. Each month of the decade has a different name.

I'm sort of looking for something with a different vibe when it comes to the coprime number.