720,?,120,30,6,1

Let's look at the reverse sequence.  In other words, let's 
start with the 1 and go backwards:

1,6,30,120,?,720

To get from 1 to 6, we multiply 1 by 6
To get from 6 to 30, we multiply 6 by 5
To get from 30 to 120, we multiply 30 by 4
So following that pattern, we multiply 120 by 3, to get 360,

To see if it works all the way, we follow that pattern and 
multiply 360 by 2, and get 720.  So the pattern works.  The missing
number is 360.

720,360,120,30,6,1

Edwin