Mental Arithmetic Aids

A number will divide by :

2 when the last figure is even

3 when the sum of the digits can be divided by 3

4 when the last 2 figures can be divided by 4 or are 0's

5 when the last figure is 5 or 0

6 when the last figure is even or 0 -AND- the sum of the digits will divide by 3

7 when the number is composed of 6 figures all alike;
when composed of six figures of which the first three are like the last 3 e.g. 421421

8 when the last 3 figures can be divided by 8 or are 0's

9 when the sum of the digits can be divided by 9

25 when the last 2 figures are 0's or will divide by 25

PUZZLE - but I don't know a way of working this out, even though I know the answer :
There is a number less than 3000, what is it ?
you can divide it by
10 and get a remainder of 9
9 and get a remainder of 8
8 and get a remainder of 7
7 and get a remainder of 6
6 and get a remainder of 5
5 and get a remainder of 4
4 and get a remainder of 3
3 and get a remainder of 2
2 and get a remainder of 1
( a platoon of soldiers with this number of men could never stand in a rectangular formation, there was always one missing from the corner !)