8a) Yes, but only under the circumstances where m & n are multiples of 2 (even numbers), hence it is possible to divide both m & n by 2 completely and form a whole number of 2cm x 2cm squares with no remainder.

8b) To find the number of ways to split this rectangle into squares, we need to find the number of common factors between 280 and 145:

280=1x2x2x2x5x7
145=1x5x29

As such these 2 numbers only have 2 commin factors, 1 and 5, and it is only possible to split this rectangle into squares in 2 ways.