G1.4 Using numbers: $1,2,3,4,5,6$ to form a six-digit number: $A B C D E F$ such that $A$ is divisible by $1, A B$ is divisible by $2, A B C$ is divisible by $3, A B C D$ is divisible by $4, A B C D E$ is divisible by $5, A B C D E F$ is divisible by 6 . Find the greatest value of $A$.
$\overline{A B C D E}$ is divisible by $5 \Rightarrow E=5$
$$
(A, C)=(1,3) \text { or }(3,1)
$$
$\because \overline{A B}$ is divisible by $2, \overline{A B C D}$ is divisible by $4, \overline{A B C D E F}$ is divisible by 6
$\therefore B, D, F$ are even.
$\overline{A B C}$ is divisible by $3 \Rightarrow 1+B+3$ is divisible by $3 \Rightarrow B=2$
$$
\Rightarrow(D, F)=(4,6) \text { or }(6,4)
$$
$\overline{A B C D}$ is divisible by $4 \Rightarrow \overline{C D}$ is divisible by 4
When $C=1, D=6 \ldots$ (1)
When $C=3, D=6 \ldots$ (2)
$$
\begin{array}{l}
\Rightarrow F=4 \\
\therefore \overline{A B C D E F}=\overline{A 2 C 654}
\end{array}
$$

Greatest value of $A=3$