The new numbers after subtracting remainders are:

2011-9 = 2002

2623-5 = 2618

Prime factors of 2002= 2 × 7 × 11 × 13

Prime factors of 2618 = 2 × 7 × 11 × 17

Therefore HCF of 2002 and 2618 is: 2 × 7 × 11 = 154

Hence the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively is 154