## Visualizing Factors and Prime Factorization.

**Update 8/2014:** The calculator discussed below is also available in the Chrome store here (for free of course).

I’ve previously discussed Brent Yorgey’s factor diagrams. As the father of a 6 year old, I’ve found they are a great way to introduce the concepts of primes and factorization.

Since then, I dabbled with the javascript animations by Sean Seefried to create 2 related products:

1. a calculator, and

2. a factorization game.

**Factor Diagram Calculator**

The calculator does multiplication and division and allows the young ‘uns to explore the diagrams. I also recently added the ability to do exponentiation after watching Mike Lawler’s video on powers of 3 and Sierpinski’s triangle.

Multiplication:

Division:

Calculator is here.

**Factorization Game
**Kids learn by playing, that is well known. So how to make a game out of all of this? I scripted up something simple whereby you’d be presented with a large number and have to factor it while the clock is ticking. Do this a few times, get a score. Then compare with friends collect badges, etc. That last bit (prizes, badges) is not written and is a whole separate app of course.

Game is here.

So as it now stands it is simple, a germ of an idea really. Any thoughts on how to improve the learning experience?

It’s weird that you have to type the last number, when it already is showing. Also, when you’re trying to go fast, it would be nice to have new game highlighted so you can just hit enter, instead of clicking on it. I like it. I would also recommend having the really large primes come up less frequently. I’m curious how it’s programmed. Is it random numbers? Or are the primes picked randomly somehow?

Thanks for the feedback!

Re: typing the last number. It is a little weird typing it in, but that last number really is a factor and having children type it in drives that home.

I think you could hit tab to go to the button without having to click on it. In any event the clock is not running at that point so your ‘score’ is not being affected.

The starting number is a random number between 5 and 500. Primes are excluded. It is interesting how often large prime factors are involved, but then that reflects the true distribution of prime numbers and so is actually a very gentle introduction to number theory and the distribution of primes. Of course to be totally honest, I shouldn’t exclude primes from the random number selection, but then the games get confusing if you start with a prime.

Bob

I love the calculator! But I can’t figure out how to do the timed game — for some reason I can type in the first number but not anything else. Granted, I’m not very good at factorization yet, so it may be me. All in all, a cool idea!

Thanks for checking it out Malke.

Curious what OS and browser you’re using. It works on several browsers on Mac and Windows that I’ve tried. You need to hit enter after each factor. I also added instructions to make it all a little clearer.

As to “I’m not very good at factorization”, well that’s what the game is for! Children who struggle with factorization should find this game helps them get a better grasp of it.

Thanks! The instructions really help and it turns out I’m great at factorization!! lol. Thanks for this – the more kids can see numbers this way the more it’ll become second nature, me thinks.

I love the visuals, and how entering a factor changes the visual. Very cool! I wish, though, that playing were more about strategy than being correct… I’m wondering about a game for two players where each can change things toward conflicting goals. What if one player can change a single factor while the other can change either the goal or the factor in the smaller groups, or something of that sort ? Hard to figure out how it will work well, but the visual suggests that different changes can be made?

Peter – Thanks for the comment!

A 2 player game is a provocative idea. Of course since there is only 1 keyboard you’re dealing with an on-line networked game (lots of work), or perhaps a tablet game where people take turns like with chess.

But leaving aside the implementation issue…

Perhaps something around common factors? Each player gets their own number. A common factor is removed from the opponent’s number whereas a non-common number is only removed from one’s own… Something to noodle on. If we got something good, I’d be willing to code it up when I had some time.

Interesting game, Woodley. But 1 is not a prime…?

Murray – Yes, I should clean up the end conditions for that game to clarify that.

Thanks Robert- I enjoyed that. I can see myself using that with young students after having made factor trees together.