Question

Find the largest number which divides $320$ and $457$, leaving remainders $5$ and $7$ respectively.

Answer 1

The largest number which divides $320$ and $457$ leaving remainders$5$ and $7$ respectively

$=$ HCF of $(320-5)$ and $(457-7)$

$=$ HCF of $315$ and $450$

$450=315\times 1+135$

$315=135\times 2+45$

$135=45\times 3+0$

$\therefore$ HCF of $450$ and $315$ is $45$.

So, the largest number which divides $320$ and $457$ leaving remainders $5$ and $7$ respectively is $45$.