How should I understand the definition of [computational problem](https://en.wikipedia.org/wiki/Computational_problem)?

> A computational problem is a mathematical object representing a
> collection of questions that computers might be able to solve. For
> example, the problem of factoring
> 
> "Given a positive integer n, find a nontrivial prime factor of n."

What is the mathematical object in the example above? Quoting Wikipedia again:

> Commonly encountered mathematical objects include numbers,
> permutations, partitions, matrices, sets, functions, and relations.

So how can you 'represent' a collection of questions with numbers or permutations, matrices etc.? What is meant here is probably the following collection of sentences:

'find a nontrivial prime factor of 1', 'find a nontrivial prime factor of 2' and so on...

But the thing is - these sentences are not mathematical objects.

A little further in the article it reads:

> A computational problem can be viewed as an infinite collection of
> instances together with a solution for every instance.

which makes perfect sense, but I don't quite see the relationship with the first definition.