I would recommend removing "7" from the board at all. The easiest opening move is to just start clicking all the 7s (since that guarantees you all multiples of 7 until you run out of 7s).
This strategy requires 0-thinking and is a bit tedious. If the board has no 7's on it, you're required to add from the get-go.
EDIT: Also, very fun little game. Thanks for sharing!