# The Factor/Multiple Game

As far as I'm aware, this is not a super well-known game. I first learned of it from Ian Stewart's ``Professor Stewart's Hoard of Mathematical Treasures.''

## Description

Alice and Bob take turns saying whole numbers (let's assume Alice goes first) according to the following rules.
- Every number said (besides the first) must be a factor or multiple of the previous number said.
- Once a number has been said, it may not be said again for the duration of the game.
- Alice must begin with an even number as their first move.

If a player ever has no legal moves left, they lose.

e.g. \( 98 (A) \rightarrow 49 (B) \rightarrow 7(A) \rightarrow 77 (B) \rightarrow 11(A) \rightarrow 55(B) \rightarrow 1(A) \rightarrow 97(B) \)