Game of numbers

Alice and Bob love playing games, and this time they are playing with an array of $N$ integers. They take turns alternatively, with Alice having the first turn. In a player's turn, the player can pick any number (say $x$) which is greater than 1 from the array. Then the player transforms the number $x$ into $(x \times i) / p$, where $p$ is any prime number which divides $x$ and $i$ is an integer i