Find the largest number which divides $245$ and $1029$ leaving remainder $5$ in each case.

Subtract $5$ from each number and then find the H.C.F.

$245-5=240$ and $1029-5=1024$

H.C.F$(240,1024)$ by Euclid's division lemma $a=bq+r$

$a=1024,b=240$

$1024=240\times 4+64$

$240=64\times 3+48$

$64=48\times 1+16$

$48=16\times 3+0$

H.C.F$=16$

Hence the required number $=16$