53. Use $0,1,2,3,4,5,6$ once each to form a seven-digit number, such that this number is a multiple of 165. The largest number is $\qquad$
Answer: 6431205
Solution: It is easy to know that $165=3 \times 5 \times 11$,
Since
$0+1+2+3+4+5+6=21$ is a multiple of 3,

Therefore,
any seven-digit number formed by these 7 digits must be a multiple of 3.

Also, since the seven-digit number is a multiple of 5, the last digit must be 0 or 5, to get the largest number,
it should be $65 \times \times \times \times 0$;
But this seven-digit number is a multiple of 11, and $6-5=1$,
the difference of the sums of any two numbers taken from $1,2,3,4$ must be one of $0, \pm 2, \pm 4$,

so it cannot be a multiple of 11;
If the seven-digit number is taken as $645 \times \times \times 0$,

since the sum of the digits in the odd positions $>6+5=11$, and the sum of the digits in the even positions $<11$,
it cannot be a multiple of 11 either;
If the first three digits of the seven-digit number are taken as $643 \times \times \times 0$, it cannot be a multiple of 11 either, and can only be taken as $643 \times \times \times 5$, at this point it can be 6431205, which is the largest among the seven-digit numbers.