Prime versus Composite

 Visualizing prime and composite numbers can be very difficult for students. They are usually taught that prime numbers only have factors of one and themselves while composite numbers can have more than those two but what does that mean visually.  I didn’t know a way to provide a visual representation that shows the difference between prime and composite numbers.  

The idea is that if a number is prime, you cannot arrange it in any rectangular or square shape other than in a 1 by the number.  It doesn’t matter if it is vertical or horizontal, it’s still in a 1 x whatever arrangement.

If you look at the picture to the left, you’ll notice I chose 11 which is a prime number and can only be expressed as 1 by 11,  If you try to arrange it any other way, you will not get a proper shape such as in the photo to the right.

I tried it in threes but no matter how you arrange the blocks.

On the other hand composite numbers can be arranged in more than one way.  Take the number 20.  It is a composite number and can be arranged in multiple ways.  It can be done as 1 x 20, 2 x 10, 5 x 4, or 4 x 5, 10 x 2, or 20 x 1, so the factors are 1,2,4,5,10,20.  You can see the results are perfect shapes.

So as far as visualizing, composite once can arrange representations in complete shapes while those for prime numbers only work in a 1 x the number.  

When I looked at the visual, I was surprised to see the current definitions make sense when you look at the photos.  Since I read the definition, I’ve used it and many of my students had light bulbs go off. They went “oh!”  

I’ve even used this as a hands on activity where I gave students some single blocks and 10 blocks to work on finding different ways of making say 20 or 43. They play around and end up concluding prime numbers can only be done in one shape while composite do others.

So the next time you have to revisit prime versus composite numbers, try this to help them see the difference.