In the multiplication shown, the letters $A, B, C$ and $K(A<B)$ represent different
\begin{tabular}{lll} 
& $A$ & $C$ \\
$\times)$ & $B$ & $C$ \\
\hline$K$ & $K$ & $K$
\end{tabular}
integers from 1 to 9 .
(Hint: $K K K=K \times 111$.)
G8.1 Find $A$.
G8.2 Find $B$.
G8.3 Find $C$.
G8.4 Find $K$.
$$
1^{2}=1,2^{2}=4,3^{2}=9,4^{2}=16,5^{2}=25,6^{2}=36,7^{2}=49,8^{2}=64,9^{2}=81
$$

Possible $K=1,4,5,6,9$
$100 K+10 K+K=111 K=3 \times 37 K, 37$ is a prime number
Either $10 A+C$ or $10 B+C$ is divisible by 37
$$
10 B+C=37 \text { or } 74
$$

When $B=3, C=7, K=9$
$$
999 \div 37=27
$$
$$
\begin{array}{l}
\therefore A=2 \\
B=3 \\
C=7 \\
K=9
\end{array}
$$