Answer:
yes, for positive numbers
Explanation:
You want to know if the number of arrays that represent a number is equal to the number of factor pairs of that number.
Assumptions
We assume that we're only concerned with Natural numbers (positive integers).
We assume that the factor pair 2×3 is indistinguishable from the factor pair 3×2, and that an array of 2 rows and 3 columns is indistinguishable from an array of 3 rows and 2 columns.
Arrays
Each array corresponds to a factor pair. One factor of the pair specifies the number of rows; the other factor specifies the number of columns. The product of those factors is the number of interest.
Example
12 = 1·12 = 2·6 = 3·4 . . . . . factor pairs listed with smallest factor first
The attachment shows arrays associated with these factor pairs.
If the number is a square number, then there will be an odd number of divisors. One of the divisors is repeated to make the factor pair. This results in a square array as one of the arrays that represent the square number. The second attachment shows arrays for the square number 9.
There will be as many arrays as there are factor pairs.