987654321 = 8 x 123456789 + 9
98765432 = 8 x 12345678 + 8
9876543 = 8 x 1234567 + 7
987654 = 8 x 123456 + 6
...
9 = 8 x 1 + 1

Explain why this pattern holds in other number systems using bases other than base 10.

For example in base 4

321 = 2 x 123 + 3
32 = 2 x 12 + 2
3 = 2 x 1 + 1