Question

Find the greatest number which divides $425$ and $373$, leaving remainders $2$ and $4$ respectively.

Answer 1

Greatest number which divides $425$ & $373$ and leaves remainder $2$ & $4$

$x=425-2$ $\Rightarrow 423\Rightarrow$

$y=373-4\Rightarrow 369$

Factorize $x=3\times 3\times 47$

Factorize $y=3\times 3\times 41$

$\therefore$ greatest number which divides $=9$.