9 Digits
Can you find a 9-digit number, which uses each of the digits 1,2,3,4,5,6,7,8,9 once only that is divisible by 9
And .... when the last digit is removed the 8-digit number is divisible by 8
And .... when the last digit is removed the 7-digit number is divisible by 7
etc.
You might find it easier to start with a 1-digit number which divides by 1 (Plenty of choice here)
Then a 2-digit number which divides by 2 (Not quite so much choice)
Then a 3-digit number which divides by 3 (Use the fact that if a number divides by 3 then the sum of the digits divides by 3. Eg 123 divides by 3 because 1+2+3=6 divides by 3, but 241 doesn't because 2+4+1=7)
And then .... how easy is it to use the tenth digit, 0, to turn the nine digit number into a ten digit number that divides by 10?