The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.

• Player 1 chooses a number on the game board by clicking on it. The square will be colored blue, as shown for 12. Player 1 receives 12 points for this choice.
• Player 2 then clicks on all the proper factors of Player 1’s number. The proper factors of a number are all the factors of that number, except the number itself. For example, the proper factors of 12 are 1, 2, 3, 4, and 6. Although 12 is also a factor of 12, it is not considered a proper factor. All of the proper factors that Player 2 selects will be colored red. Player 2 will receive 1 + 2 + 3 + 4 + 6 = 16 points for selecting all of the proper factors.
• Players reverse roles. On the next turn, Player 2 colors a new number and gets that many points, and Player 1 colors all the factors of the number that are not already colored and receives the sum of those numbers in points.
• The players take turns choosing numbers and coloring factors.
• If a player chooses a number with no uncolored factors remaining, that player loses a turn and does not get the points for the number selected.
• The game ends when there are no numbers remaining with uncolored factors.
• The player with the greater total when the game ends is the winner.

Here’s a lesson that integrates the game.