Eric had 13 tiles to arrange in a rectangular design. He drew a model of the rectangles he could make with the 13 tiles?
How does Eric's drawing show that 13 is a prime number?
13 is a prime number
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To understand how Eric's drawing shows that 13 is a prime number, we need to consider the possible rectangular designs he could create with his 13 tiles.
Since Eric wants to arrange his tiles in a rectangular design, he must find two numbers whose product is equal to 13. Let's examine all the possible combinations of two numbers that multiply to give 13:
1 x 13 = 13
13 x 1 = 13
As you can see, these are the only two combinations. Both options result in a rectangle of size 1 by 13 (or 13 by 1), which represents a single-row or single-column layout respectively.
If 13 were not a prime number, we would have more options. For example, if 13 were a composite number (a number that can be factored into smaller whole numbers), it could be expressed as a product of two different numbers greater than 1. However, since 13 only has two distinct factors (1 and 13), it cannot be expressed as a product of two whole numbers other than 1 and itself.
Therefore, Eric's drawing showing only one possible rectangular design (1 by 13 or 13 by 1) demonstrates that 13 is a prime number.