If 15 × 14 × 13 × ... × 3 × 2 × 1 = 3^m x n where m and n are positive integers, then what is the maximum value of m?

1. **Identify the Structure**: The expression $15 \times 14 \times \dots \times 1$ is simply $15!$ (15 factorial). The equation is $15! = 3^m \times n$. We need to find the maximum $m$, which mean