The best way to practice math is to play with it — to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

So this art project is a great way to practice multiplication. Use the prime factors of numbers from one to one hundred to create a colorful design.

### Start with a Hundred Chart

First, download this printable file of hundred charts in non-photo blue (or light gray, if you’re printing in grayscale). The file includes:

- Line-by-line traditional chart, counting from top to bottom.
- Line-by-line bottom’s-up chart, counting from bottom to top.
- Ulam’s Spiral chart, spiraling out from the center.
- Blank grids for making your own patterns.

Decide whether you want to work in straight lines or in a spiral — or in any random pattern you like. Print the hundred chart that fits your artistic vision.

Or, if you feel especially creative, use a long ruler or drafting square to draw a grid on art paper. Make it as big as you like — you’ll never run out of numbers!

### Prime Factor Coloring Rules

Choose a neutral color for the 1 square. Then choose brighter, distinct colors for 2 and 3, the first two prime numbers. Pick your favorite color for 2 because it will show up the most in your design.

Color the composite numbers according to their prime factors. For example:

- 4 = 2 × 2, so divide the square into two parts and color both parts with your color for the number 2.

- 5 is prime, so it gets a new color of its own.

- 6 = 2 × 3, so divide the square into two parts and color one part with your color for 2 and the other for 3.

- 7 is prime, so it gets a new color of its own.

- 8 = 2 × 2 × 8, so divide the square into three parts and color each of them with your color for 2.

- 9 = 3 × 3, so divide the square into two parts and color both parts with your color for 3.

- 10 = 2 × 5, so divide the square into two parts and color one part with your color for 2 and the other for 5.

- 11 is prime, so it gets a new color of its own.

- 12 = 2 × 6 = 2 × 2 × 3, so divide the square into three parts and color two of the parts for 2 and the other for 3.

Continue along the chart, figuring out the prime factors of each number (the smallest numbers you can multiply to get it, not counting 1). Split that number’s square so you can color one section for each factor.

### More Ways to Play

For students who haven’t studied prime factors before, here is a fun way to teach them:

Not feeling artistic? Try these math games:

And check out all the wonderful ways to play with a hundred chart in this reader-favorite post:

### Credits

This math art project was inspired by Natalie Wolchover’s beautiful spiral creation:

Check out my color map of the numbers 1 through 324. The white square in the center = 1, the blue square = 2, & the numbers spiral out from there (an “Ulam spiral”). Squares representing primes have unique colors, other squares are divided into the colors of their prime factors. pic.twitter.com/Z07TQSIb7X— Natalie Wolchover (@nattyover) August 31, 2020

Feature photo (top) by Washington Oliveira 🇧🇷 via Unsplash.com.