# Prime and Composite Numbers

This Math Investigation is coming to you a little early. I wanted you all to see what it will look like as you start your Math adventure this summer.

Knowing prime and composite numbers are extremely helpful throughout Math, especially with division and fractions.

To begin, we need to know what factors of a multiple are. Wait! What is a factor and what is a multiple?

PRIME numbers have only 2 factors: 1 and itself.

COMPOSITE numbers have many factors. 6 is a multiple of 2 x 3 and 6 x 1.

Let’s look at 2…prime or composite? It’s factors are 1 and 2, that’s it! Therefore it is a PRIME number.

What about 3? If you look at your multiplication chart, where else do you see a 3? You only see it with 1 x 3 and 3 x 1. Therefore 3 is a PRIME number.

How about 4? 4 has 2 factor pairs: 1 x 4 and 2 x 2. Multiple factors! It is a COMPOSITE number.

Using the colorful 100s chart below, print and cut out all those pieces. You are going to use these pieces to make rectangles to show prime and composite numbers. There are a lot of pieces, but this is also great practice using our fine motor skills by cutting with precision. Store the pieces in a baggie or an envelope to use later. If you can’t print these out, use beans or pasta, rocks or pennies. Anything can be used as a marker!

If you can make a rectangle that is full and filled in, and it does not only have a factor (or a side) of 1, then it is a composite number.

Let’s look at the number 12. Can you make a rectangle with 12 pieces?

15 is a COMPOSITE number because it can made by multiplying 1 x 15 and 5 x 3.

Let’s look at 17. How can we make 17?

Does 17 make a full rectangle? It does not. The only way to make 17 is to multiply it by 1. It is a PRIME number.

In your math journal, circle all the prime numbers on the multiplication chart. Use the rectangular pieces to find all the prime and composite numbers. Take your time, and have fun!

Next, go to your “Daily Work” section of your journal, and sketch out as many rectangles as you can for composite numbers 24 and 36.  Use a ruler to make straight lines, and remember to label the factors (sides).

If you would like to share you work, send me a photo of your work!

Want to do a little research? What about the number 1…is it a prime or composite number? It doesn’t have multiple factors just 1 x 1, but 1 is the only factor in the factor pair. This was debated by the Greeks long ago. If you want to know if the number 1 is a prime number, read https://en.wikipedia.org/wiki/Prime_number and go to the section labeled “Primality of one.”