Whole numbers can be represented by rectangular arrays of tile.
What kind of numbers have more than one rectangular array?
Prime numbers
Numbers that have more than one rectangular array are factors or multiples of a given number.
To understand this concept, let's start by defining factors and multiples:
- Factors: Factors are numbers that can divide into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiples: Multiples are numbers that can be obtained by multiplying a given number by another value. For example, the multiples of 3 are 3, 6, 9, 12, and so on.
Now, for a number to have more than one rectangular array, it needs to have more than one possible combination of factor pairs. This means that the number must have multiple factors.
Let's take the number 12 as an example. The factors of 12 are 1, 2, 3, 4, 6, and 12. When we represent 12 as a rectangular array, we can have arrays with dimensions (1 x 12), (2 x 6), (3 x 4), and (4 x 3). Each of these arrays has a different shape but can still represent the same number (12).
On the other hand, numbers that have only one rectangular array have only one possible combination of factor pairs. These numbers are called prime numbers, and they can only be divided evenly by 1 and themselves.
In summary, numbers that have more than one rectangular array (or more than one possible combination of factor pairs) are non-prime numbers, whereas prime numbers have only one rectangular array.