If a matrix has $24$ elements,what are the possible orders it can have? What if it has $13$ elements?

(N/A) We know that if a matrix is of the order $m \times n$,it has $mn$ elements.
Thus,to find all the possible orders of a matrix having $24$ elements,we need to find all the ordered pairs of natural numbers whose product is $24$.
The ordered pairs are: $(1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6),$ and $(6, 4)$.
Hence,the possible orders of a matrix having $24$ elements are: $1 \times 24, 24 \times 1, 2 \times 12, 12 \times 2, 3 \times 8, 8 \times 3, 4 \times 6,$ and $6 \times 4$.
Similarly,for $13$ elements,we find the ordered pairs of natural numbers whose product is $13$. Since $13$ is a prime number,the only pairs are $(1, 13)$ and $(13, 1)$.
Hence,the possible orders of a matrix having $13$ elements are $1 \times 13$ and $13 \times 1$.