Divides by 6?

To be divisible by 6 the number must be divisible by 3 and it must be even. If a base 3 number ends in 0 it is divisible by 3, so this number is divisible by 3. However, to be even, a base 3 number must contain an even number of odd digits, since each digit $a_n$ represents the number $a_n*3^n$ , which is only odd if $a_n$ is odd, since $3^n$ is always odd. Since this number has exactly nine odd digits (or one's) this number is odd, therefore it doesn't divide by 6.