Topological sorting of a set

Question

Given this Hasse diagram

(made from the set $A$: $\{1,2,3,4, 5,6,10,12,15,20,30,60\}$ with the relation divides).

I have to find the topological sorting of the set

$$ \begin{equation} (2,3), (4,6), (2,10), (10,2), (30,30), (2,30) \tag{*} \end{equation} $$

Normally when finding the topological sorting one of the possible sorting could be

$$ 1 \preceq 2 \preceq 3 \preceq 5 \preceq 15 \preceq 10 \preceq 6 \preceq 4 \preceq 12 \preceq 20 \preceq 30 \preceq 60 $$

My question is how and where does (*) come in?

Answer 1

Here’s the Hasse diagram of your partial order: $\langle a,b\rangle\preceq\langle c,d\rangle$ if and only if $a\mid c$ and $b\mid d$.

                         <30,30>  
                        /   |   \  
                       /    |    \  
                   <4,6>    |    <2,30>  
                      |     |     |  
                      |     |     |  
                   <2,3>  <10,2> <2,10>

Can you work from it to get a topological sort?