Divides by 143?

In order to be divisible by $143_{10}$ , the number must divide $11_{10}$ and $13_{10}$ , since, in decimal, $143 = 11*13$ .

Now, let $e = \sum (\textrm{even digits})$ and let $o = \sum (\textrm{odd digits})$ and let $s = e+o$ .

A number is divisible by $13$ in base $12$ if $(e-o)$ divides $13$ .

And a number is divisible by $11$ in base $12$ if the sum of the digits is divisible by $11$ .

In this case $e = 11$ and $o=11$ , so $e-o=0$ , which divides $13$ , so the number divides $13$ .

Also, $s=e+o=22$ which divides $11$ , so the number divides $11$ .

Since the number divides both $11$ and $13$ , the answer is... $\boxed{Yes}$ , the number is divisible by $143$ .