Possible Last Digits of Triangular Numbers

All possible last digits of triangular numbers are derived in the table.

\[n\]	\[n-1\]	\[n(n-1)\]	\[\frac{n}{2}(n-1)\]
0	1	0	0, 5
1	2	2	1, 6
2	3	6	3, 8
3	4	2	1, 6
4	5	0	0, 5
5	6	0	0, 5
6	7	2	1, 6
7	8	6	3, 8
8	9	2	1, 6
9	0	0	0, 5

By exhaustion the only possible last digits of a triangular number are 0, 1, 3, 5, 6, or 8,