Question: what is the greatest no which shall divide 305 and 629 anf leave a remainder 8 in each cases ?
Let n be this number
305 = kn + 8, where k is some (positive) integer.
629 = jn + 8, where j is some (positive) integer.
Then,
297 = kn
621 = jn
i.e. n is gcd (greatest common divisor) of 297 and 629.
297 = (3^3)*(11)
621 = (3^3)*(23)
Therefore gcd(297,621) = 27
Answer: n = 27