504:n>9

I think you mean the inequality 504 / n > 9. Here’s the solution:

• We require n ≠ 0.
• Consider n > 0: 504 / n > 9 implies 504 > 9n, so n < 56.
• For n < 0: multiplying by n would flip the inequality, leading to 504 < 9n, which cannot happen for n < 0. So no negative n work.
• If n is a natural number, 1 ≤ n ≤ 55.

Answers:

• All positive integers n: n ∈ {1, 2, ..., 55}
• Count of such n: 55
• Greatest such n: 55

If you meant something else (e.g., a different interpretation of “504:n>9” or you want the real-number solution), let me know.