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)