KMO 2006 Problem 2

Alice and Bob are playing "factoring game." On the paper, $270000(=2^43^35^4)$ is written and each person picks one number from the paper(call it $N$ ) and erase $N$ and writes integer $X,Y$ such that $N=XY$ and $\text{gcd}(X,Y)\ne1.$ Alice goes first and the person who can no longer make this factoring loses. If two people use optimal strategy, prove that Alice always win.