The first statement means: if A is a factor of BC and A and B have no common factors than A divide C.

For example A=2 B=3 and C=4. A is a factor (=divide) BC which is 12. But A and B have no common factor. Therefore A divide C (2 divides 4).

The second statements is more straightforward. It just means that if a number divides another one for example 2 divides 4, then the only way it can be divided by this number as well is that it is the same number or the opposite.

Hope this clarify things

_________________

GMAT score: 780 (51 quant, 45 verbal, 5.5 AWA, 8 IR)