Playing The Factor Game in Middle School Math


Finding the Factor Game Again!

I was looking through my middle school math folders on my computer, and came across a document called “The Factor Game,” and it occurred to me that in trying to think of some new things to do with my classes, I forgot to play the Factor Game this year when we started talking about factors!

I was so disappointed with myself. Of course, we can play it next week, or any other time, but I just couldn’t believe that I had forgotten about it.

I’m sure many people know of the Factor Game, or use a version of it, but for those who don’t, I’ll explain how to use this math game, which is great for 6th grade, but also elementary grades as well – and even 7th or 8th grades if students need factor practice!

clipboard numbered 1 to 30 to play the factor game


The Factor Game is a fantastic math game to help students practice both factors and strategy!

How to Play the Factor Game
1) Players start with a simple game board, with the numbers 1-30 (in the past I’ve alternated between giving them a pre-printed sheet and letting them write their own numbers on their own paper; sometimes I have them play at the whiteboard).

2) a. Player 1 chooses a number, and marks it (they might circle it, square it, triangle it, color it etc).Player 1 receives points equal to the number they chose.
b. Player 2 then marks all of the remaining factors of Player 1’s choice, and Player 2 gets points equal to all of the remaining factors of that number.

3) Next, Player 2 chooses a number (and gets those points), and Player 1 identifies all of the factors of that number, receiving those points.

4) Play continues this way until all possible numbers have been used.
*Special rule – players can’t choose a number that has no factors available for the other player. If they do, they lose their turn, receiving no points.

factor game board
They choose 30

Factor Game Example
When I introduce this game to my math classes, we play it on the whiteboard, and I always allow them to go first (the first time). Often, they will choose 30 as their number, since it’s the biggest.

When I go ahead and mark all the remaining factors of 30 (my points), they are shocked! After the first turn, they have 30 points and I have 42!  (I normally have 2 students record our scores on the board, while 2 others keep running totals on a calculator, but points can all be tallied at the end if you want).

factor game board
I choose 27

For my first turn, my choice would be 27.This gives students them only 9, since 1 and 3 are already gone. Needless to say, they’re usually a bit disappointed by this!


After their experience with 30 and its factors, students start thinking a bit more.

They will often consider 25 or 23, but I remind them that they must leave a factor for me, and 1 and 5 are already taken. For the sake of showing further steps, let’s pretend they choose 21. That leaves 7 for me.

They choose 21

PictureFinished Game

The game continues, alternating turns, until all possible numbers are used, as shown in the “finished game” picture.

The second time we play as a group, I choose 29 as my first number, and they are disappointed to only get 1 point!

We continue to play the second game, and they get a better idea of what makes a good choice.

Students Play the Math Game With a Partner
After our games as a class, I have the students work in partners, and they normally get one or two games played before we stop to discuss at the end of the period. We always talk about what the best and worst first choices are, and bring the idea of prime and composite into the discussion.

I’ve been playing this game with students for at least 15 years (I think), and every set of students has loved it! I found the game when I was involved with Mathline, so long ago. If you’d like to see the original lesson plan, with extension ideas, click here.

You can also watch the video below of me explaining the Factor Game. I did this on a Facebook Live and then uploaded to YouTube:-)

Have you played the Factor Game? If so what do you love about it?


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Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

  • All subject areas in 4th and 5th grades
  • Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

If you’re looking for ideas and resources to help you teach math (and a little ELA), I can help you out!



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