G1.1 Given that when 81849,106392 and 124374 are divided by an integer $n$, the remainders are equal. If $a$ is the maximum value of $n$, find $a$.
$$
\begin{array}{l}
81849=p n+k \ldots \ldots .(1) \\
106392=q n+k \ldots \ldots .(2) \\
124374=r n+k \ldots \ldots .(3)
\end{array}
$$
(2) $-(1): 24543=(q-p) n$
(3) $-(2): 17982=(r-q) n$ $\qquad$
(4): $243 \times 101=(q-p) n$
(5): $243 \times 74=(r-q) n$
$a=$ maximum value of $n=243$