Collection of multiplication puzzles

Which number or numbers, from 0-100, are described by the clues below? Further, which clues, if any, are unnecessary?

With this puzzle, it's obvious the clues could be changed to yield more puzzles. The initial set of numbers could also be something different from 0-100. In fact, given the right clues, it needn't be finite either. For example, if the initial set is 0-infinity, and your clues are, the number is even and prime, then a unique number is described, namely, 2.

Source: What Do You Need? by NRICH

Lots more puzzles can be found here.