Question

Find the greatest number which divides 2011 and 2023 leaving the remainder 9 and 5 respectively

Answer 1

2011-9=2002 and 2623-5=2618

now , find the HCF of 2002 and 2618

you will get 154.  

so the number is 154 which divides 2011 and 2623 leaving remainder 9 and 5 respectively.