Relaxing after an early dinner

Its good to have an early dinner and now I have some time to relax and think. Right now I am sitting to brown leather couch with a Jazz music playing in background and I think it's good time to ponder over some Math. There are problems of counting zero in a factorial or sometimes disguised as counting the highest power of a particular prime number which is a factor or counting the number of zeros in difference between two factorials. All these are of the same genre and can be solved similarly by adding the quotients when divided by p then p^2 then p^3 and so on.