Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively

Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.

The required number when divides 2011 and 2623 leaves remainders 9 and 5 this means $2011-9=2002$ and $2623-5=2618$ are completely divisible by the number.

Therefore, the required number = H.C.F. of 2002 and 2618

By applying Euclid’s division lemma

$2618=2002 \times 1+616$

$2002=616 \times 3+154$

$610=154 \times 4+0$

H.C.F. of 2002 and 2618 = 154

Hence, the required number is 154