Repeated Divisibility

Let me tell about a 17 digit number,which I found after several attempts,having a special property.
The number is 34880 44860 36585 69.
This number is divisible by 17.
When you delete the last digit 9,the new 16 digit number will be divisible by 16.
Continuing,when you delete the last digit 6 from this 16 digit number,the new 15 digit number will be divisible by 15 and so on,showing divisibility by 14,13,12,11....etc
I am showing below some of the quotients relating to the  divisions-
Division by 17-D/17...Quotient is 20517 91094 332857
D/16...   Number to be divided is 34880 44860 365856 .Quotient is  21800 28037 72866
D/15...   Number to be divided is 34880 44860 36585.Quotient is  23253 63240 2439
D/14...   Number to be divided is 34880 44860 3658...Quotient is 24914 60614 57
D/11..... Number to be divided is 34880 448603.Quotient is 31709 49873
D/7....... Number to be divided is 3488044.....Quotient is 498292
D/4....... Number to be divided is 3488 ..Quotient is 872
It is difficult to work out such numbers.While you can find many numbers upto 9 or 10 digits having divisibility by numbers from 2 to 10,it may be difficult to get the 11th,12th etc digits and then you have to start all over again..