Question

Find the largest number that divides $623,729$ and$841$ leaving remainders $3,9$ and $1$ respectively.

Answer 1

This means we need to find. HCF of

$623-3,729-9$ and $841-1$

$\Rightarrow 620,720,840$

$\begin{array}{c}10\\ 2\\ \end{array}|\begin{array}{ccc}620& 720& 840\\ 62& 72& 84\\ 31& 36& 42\end{array}$

$\therefore$ HCF $=10\times 2$

$=20$