A is an integer. Dividing 89 & 125 gives remainders 4 & 6 respectively. Find a?

You seem to have
  (89 - 4) and (125 - 6) are both multiples of a.
  89 - 4 = 85 = 5*17
  125 - 6 = 119 = 7*17
The value of "a" seems to be the only common divisor of 85 and 119, namely 17.