$[\underline{\text { Divisibility Criteria (other) }}]$

Find all numbers of the form $\overline{13 x y 45 z}$ that are divisible by 792.

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Apply the divisibility rules for 8, 9, and 11.

## Solution

$792=8 \cdot 9 \cdot 11$. According to the divisibility rule for $8 \mathrm{z}=6$. According to the divisibility rule for $9 x+y=8$ or 17. According to the divisibility rule for 11

$1+x+4+6-3-y-5=x-y+3=0$ or 11. Since $x+y$ and $x-y$ are of the same parity, we get two cases: $x+y=x-y=8$ or $x+y=17$, and $y-x=3$. In the first case, $x=8, y=0$, in the second case, there are no solutions.

## Answer

1380456.