Who has a winning strategy, the first or the second player? The number 328 is written on the board.  Two players alternate writing positive divisors of 328 on 
the board, subject to the following rules:


*

*No divisor of a previously written number may be written;

*The player who write 328 loses.


Who has a winning strategy, the first or the second player?
The divisors of 328 are 1,2, 4, 8, 41, 82, 164.  How to think the winning strategy?
 A: For any kind of game like this, the beginning of the analysis is always the same. You start at the end of the game and work backwards.
So, if it's my turn, which game states would force me to a loss? Now step back one turn: Which game states would let you leave a losing game state to me next turn? And so on. At some point you have reached the start of the game, and you will be the one with a winning strategy. You just have to see whether it is me or you who is the starting player.
Also, I'd advise you to focus on prime decompositions.
A: Let me help you with a visualization. 
$348=2^3\cdot 41$, 
so the divisors are $2^x\cdot 41^y$ where $0\leq x\leq 3, 0\leq y\leq 1$. 
You can find these points $(x,y)$ on a grid (given a Descartes coordinate system). 
Each player can paint one of these points red. 
The rules say that once a point is painted red, every point that is in the left lower quardrant of that point is out. 
The one who paints $(3,1)$ loses. 
Positions of the game are (allowed) subsets of the set of these eight points (that are left after deleting quadrants). 
Hopefully, this helps you finding the winning strategy according to @Arthur 's answer. 
