What is not a problem modular division is used for?

First let's define what modular arithmetic is, what would come is an arithmetic system for equivalence classes of whole numbers called congruence classes.

Now, the modular division is the division in modular arithmetic.

Answering the question, a modular division problem like ordinary arithmetic is not used, division by 0 is undefined. For example, 6/0 is not allowed. In modular arithmetic, not only 6/0 is not allowed, but 6/12 under module 6 is also not allowed. The reason is that 12 is congruent with 0 when the module is 6.