How to Play the Factor Game on a 1–49 Board

Setup

7×7 grid numbered 1–49 sequentially.

Rules (Standard Version)

1. Two players alternate.
2. Player A picks any number.
3. Player B picks a proper factor of that number (divides evenly, not the number itself).
4. Player A picks a factor of Player B's number, and so on.
5. Forced to pick 1? You lose. (1 has no proper factors.)

Strategy

• Force primes: Prime numbers only factor to 1 – great for trapping opponent.
• Think chains: Choose numbers with few factors to limit opponent's replies.
• Defense: Avoid giving opponent a number with many factor options.

Example

12 → 3 → 1 (Player A loses). Better: 12 → 4 → 2 → 1 (Player B loses).

Great for practicing factor recognition and prime intuition!