Question 811284
Do you mean the number 35X64 with X as the middle digit is divisible by 3?
 
A number is divisible by 3 if, and only if the sum of its digits is divisible by 3
{{{3+5+6+4=18}}} is already divisible by 3 since {{{18=3*6}}} .
To make {{{3+5+6+4+X=18+X}}} divisible by 3, X itself must be divisible by 3.
So to make 35X64 divisible by 3, X itself must be divisible by 3, or zero.
The possible values for X are
0, 3, 6, and 9.