These arrangements confirm 15 is composite, as it forms two rectangles (3 by 5 and 1 by 15), showing it can be evenly divided into smaller whole numbers, distinguishing it from prime numbers.
To illustrate that 15 is a composite number, let's consider two different rectangles that can be formed using 15 squares.
Firstly, arrange the squares in a rectangle with dimensions 3 by 5. You can visualize this as a rectangle with three squares along one side and five squares along the other side. The total number of squares in this arrangement is 3 * 5 = 15.
Secondly, consider a rectangle with dimensions 1 by 15. This rectangle has one square along one side and fifteen squares along the other side. Again, the total number of squares in this arrangement is 1 * 15 = 15.
These two different arrangements demonstrate that 15 can be evenly divided into smaller whole numbers, confirming its composite nature. In contrast, a prime number would only allow for a single rectangle with dimensions 1 by the number itself.