Question

Find the greatest no. leaving remainder $5$ which divide $245$ and $1029$.

Answer 1

We have to subtract $5$ from each number and then find the H.C.F

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

H.C.F of $240$ & $1024$ by Euclid division lemma$(a=bq+r)$

$a=1024$ & $b=240$

$a=bq+r$

$1024=240\times 4+64$

$240=64\times 3+48$

$64=48\times 1+16$

$48=16\times 3+0$

H.C.F$=16$

Hence the required number is $16$.