Question

Show that 12^n cannot end with the digit 0 or 5 for any natural number 'n'.

Answer 1

natural number n.

$12^n\\\\12^0=1\\12^1=12\\12^2=144\\12^3\ ends\ with\ 8\\12^4\ ends\ with\ 6\\12^5\ ends\ with\ 2$

And the units digit of $12^n$ will be : 1, 2, 4, 8, 6, 2, 4,  8, 6 ....