Find the greatest number which divides $\displaystyle 764$ and $\displaystyle 1198$, leaving remainders $\displaystyle 8$ and $\displaystyle 10$ respectively.

\(\displaystyle 764-8=756\) and \(\displaystyle 1198-10=1188\) \(\displaystyle 756=2^{2} \times 3^{3} \times 7\) \(\displaystyle 1188=2^{2} \times 3^{3} \times 11\) H.C.F. \(\displaystyle (756,1188)=2^{2} \times 3^{3}=108\) ∴ Required greatest number is 108.