GCD

A number that divides 2011 with remainder 9, will divide (2011-9)=2002 with no remainder. Similarly the same number will divide (2623-5)=2618. Thus the number is the GCD of 2002 & 2618. $2002=2\times 7\times 11\times 13 \\2618=2\times 7\times 11\times 17 \\ \therefore \text{ the GCD is }2\times 7\times 11=\boxed{154}$ or the Euclidean Algorithm can be used to find the GCD.