In cartesian product, is the order of factors important? For example- $\{1,3\} \times \{1,2\}$. Here $4$ elements will be formed. So if i write $\{1,2\}$ before $\{1,3\}$, is there any difference?

Yes, the elements of a Cartesian product are ordered tuples.
The Cartesian product is not commutative.   The order of its operation is significant. 
$$\rm \forall A\neq\emptyset~,\forall B\neq\emptyset\qquad A\neq B~\to~ A\times B\neq B\times A$$
As per your example:
$\{1,3\}\times\{1,2\} = \{(1,1),(1,2),(3,1),(3,2)\}$
$\{1,2\}\times\{1,3\} = \{(1,1),(1,3),(2,1),(2,3)\}$
Since the order in the tuples is significant, these are not the same sets.

If, however, you meant the order of the tuples within the product; the product is a set so that is not important.
$\{(1,1),(1,2),(3,1),(3,2)\}=\{(1,1),(3,1),(1,2),(3,2)\}$ et cetera.
