Is 87656432 divisible by 4? is there a shortcut? 98765432 divisible by 6? shortcut? 87654312 divisible by 8? shortcut? 278949 by 11? shortcut? 87654395 by 12? shortcut? 87654385 by 15? shortcut? you!

Hope this isn't too confusing

All of the numbers have different shortcuts.
1. Yes. Divisible by 4: if last two digits are divisible by 4 then the whole number is yes)
2. No. Divisible by 6: it must be even and when you add them up, (44) it must be divisible by 3 (no, 44 is not divisible by 3)
3. Divisible by 8: ( last 3 numbers are divisible by 8 (312) = 39 ( yes it is)
4 Yes. Divisible by 11: ( sum of digits at odd places and sum of digits at even spaces,is either 0 or divisible by 11) yes, 278949. (2+8+9) + (7+9+9)= 19 + 25 = 44 and 44 is divisible by 11)
5. No. Divisible by 12 (divisible by 3 and 4, sum of digits is divisible by 3 ; and last 2 digits divisible by 4: 87654395 : 52/3= 18 (yes) 95/4(no) this number not divisible by 12
6. No. Divisible by 15: divisible by 3 and 5 ..87654385 = 46/3 = 15..(No) divisible by 5 yes. The number is not divisible by 15