## Factorization diagram cards are here!

It’s been a long process, but factorization diagram cards are finally available for purchase!

If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading.

## History

As explained in this original blog post from 2012 and this follow-up post, the basic idea behind factorization diagrams is to visualize the prime factorization of a positive integer $n$ by taking $n$ dots and recursively grouping them according to the prime factors. For example, $30 = 2 \times 3 \times 5$ can be visualized by making two groups of three groups of five dots, as seen in one of the cards above. You can find a lot more information about factorization diagrams here, including links to related things people have made, posters for sale, and so on.

Very early on I heard from teachers who had printed the diagrams, cut them out into cards, and used them successfully in their classrooms. After hearing that, I decided that there really ought to exist a high-quality deck of factorization diagram cards for purchase. It’s taken four years for that idea to come to fruition, but they are finally here!

## The deck

So, what’s in a deck, you ask? Each deck contains 54 large (3.5 inch) square cards. The front of each card has a factorization diagram, and the back has the corresponding number and factorization written out. Numbers with multiple distinct prime factors have multiple cards with different diagrams, one for each distinct permutation of the prime factors. (For example, $12 = 2 \times 2 \times 3 = 2 \times 3 \times 2 = 3 \times 2 \times 2$ has three different cards, as illustrated below.)

You can buy your very own deck through The Game Crafter for $13.99 (see below for an explanation of the price). The images used to make the cards are freely available here (in case you’d rather just print them yourself, or do something else with them), and the source code is on github. Everything is released under a Creative Commons Attribution 3.0 license, which basically means you can do whatever you want with the source code, images, design, etc., as long as you credit me as the source (preferably by linking to https://mathlesstraveled.com/factorization). If you end up using these cards in a classroom and come up with any fun activities/games/puzzles using the cards, please let me know! I would like to collect a big list of suggested activities for different ages and eventually be able to publish the list along with the cards. ## Pricing and print-on-demand As mentioned above, I have published the deck through The Game Crafter, who have done a great job. The process was easy and professional, and I am pleased with the final product—and I hope you will be too. You might think$13.99 is steep for a deck of cards, but (a) the print-on-demand model means there are no economies of scale to be had, and (b) these are definitely high-quality cards (3.5" square, high-quality card stock, with a linen texture and UV coating that reduces glare). I think a deck should last you a while, even if young kids are handling it.

Speaking of economies of scale though, if you are—or know—an educational/game publisher who would be interested in publishing this deck at a lower price point, please contact me! Until something like that happens though, I don’t have the resources—temporal or financial—to be able to coordinate a larger print run. The print-on-demand model means that I can get these cards out without a huge commitment.

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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### 2 Responses to Factorization diagram cards are here!

1. goldenoj says:

Was trying to imagine a game with these.

First thought is always War, right? On a tie, the next card determines winner by GCF with the first card. Tied on 30, next card a 6 would beat an 8.

Can add a little thought by keeping a hand of three cards, you choose which to play for the battle.

• Brent says:

Yeah, I think something like this could definitely work!