Question

Find the largest number which exactly divides $280$ and $1245$ leaving remainders $4$ and $3,$ respectively.

Answer 1

To find the largest number which exactly divides $280$ and $1245$ leaving remainders $4$ and $3$ respectively, we subtract $4$ and $3$ from $280$ and $1245.$

$280-4=276$
$1245-3=1242$
$276=2\times 2\times 3\times 23$
$1242=2\times 3\times 3\times 3\times 23$
$HCF=2\times 3\times 23=138$
Therefore, the largest number which exactly divides $280$ and $1245$ leaving remainders $4$ and $3$ respectively is $138.$