Step 1: Concept
This is a factorial-based sequence or a division sequence where each term is divided by a decreasing integer.
Step 2: Meaning
Reading from right to left, we see: $1 \times 6 = 6$; $6 \times 5 = 30$; $30 \times 4 = 120$.
Step 3: Analysis
Continuing this increasing multiplication: $120 \times 3 = 360$. To check the final step, $360 \times 2 = 720$.
Step 4: Conclusion
The missing number is $360$, as it fits the progression of dividing the previous number by $n, n-1, n-2...$.
Final Answer: (C)