Emily wants to make a rectangular model with a height of one connecting cube. She wants to make the model in exactly 2 different ways. How many connecting cubes could Emily use to make the model in only two ways
Seems to me the answer is 6, because the rectangle can then only be made in the following two ways: (1) 6x1x1 or (2) 3x2x1. In each case, the height is 1.
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To find the number of connecting cubes Emily could use to make the model in exactly 2 different ways, we need to determine the factors of the number of cubes.
Let's consider a rectangular model with a height of 1 connecting cube. In this case, the number of connecting cubes can be represented by the equation:
Number of cubes = Length x Width x Height
Since the height is fixed at 1, we can simplify the equation to:
Number of cubes = Length x Width
Now, we want to find the number of cubes where the model can be made in exactly 2 different ways. This means we are looking for a number that has exactly 2 factors.
To have exactly 2 factors, the number needs to be a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
Therefore, the number of cubes Emily could use to make the model in only two ways would be any prime number.