it is divisible by 6

and

when the final digit is removed it becomes a 5-figure number divisible by 5

and

when the final digit is removed again it becomes a 4-figure number divisible by 4

and

when this is repeated it becomes a 3-figure number divisible by 3

and

when it is repeated again it becomes a 2-figure number divisible by 2?

Of course when it is repeated for a last time it will naturally be 1-figure number divisible by 1.