Usage of 'that' or 'those'

This is correct.


This is not correct.

In the correct (first) sentence, "that are not divisible by 2" is a modifier. Modifiers often start with the word "that" - for instance, 'I ate a watermelon that had no seeds.'

When a modifier starts with 'that', it typically describes the closest noun before the modifier. In the correct sentence, that noun is 'integers'. This makes sense, because 'not divisible by 2' is a description of the type of integers you're looking for.

In the incorrect (second) sentence, you have a run-on sentence. 'Odd numbers are integers' is a complete sentence, and 'Those are not divisible by 2' is a complete sentence (they each have a subject and a verb.) You can't join two complete sentences together without having some kind of additional word to connect them.