Number Duel Games
Prime Factor Game
The Prime Factor Game is a turn-based strategy game built around prime numbers. A composite number appears on screen. You and the bot take turns picking one of its prime factors. Each pick divides the number, shrinking it toward 1. Whoever picks the factor that brings the number to 1 wins the round.
How to Play
- A number appears at the top of the screen (for example, 60).
- Tap one of the available prime factor buttons. For 60, you can pick 2, 3, or 5.
- The number divides by your choice. If you picked 3, the number becomes 20.
- The bot takes its turn, then play passes back to you.
- Whoever reduces the number to 1 wins.
What Are Prime Factors?
A prime number is a number greater than 1 that has exactly two divisors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23. Every whole number greater than 1 can be written as a product of primes. For example, 60 = 2 × 2 × 3 × 5. These are its prime factors.
When you pick a prime factor in the game, you remove one copy of it from the number. If the number is 60 and you pick 2, it becomes 30 (because 60 ÷ 2 = 30). If you pick 3, it becomes 20. The game continues until all prime factors have been removed and the number reaches 1.
Strategy Tips
- Count the total number of prime factors (including repeats). If it is odd, the first player can win with optimal play.
- When the number has only one prime factor left (it is a prime power), whoever picks it wins. Plan ahead to be that player.
- Sometimes the best move is not the smallest factor. Think about what position you leave for the opponent.
- On Hard difficulty, the bot plays perfectly. You will need to calculate the full game tree to win.
Three Bot Difficulties
Easy bots pick random factors, giving you room to learn the rules. Medium bots use a heuristic that prefers moves leading to better positions. Hard bots use minimax search with memoization, meaning they play optimally. If you can beat the Hard bot, you understand prime factor strategy.
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- Number Duel - arithmetic strategy board game
- Nerdle - daily equation guessing game
- Math Bingo - number bingo
- Number Sense Game - number concepts