Why remainders of division give base expression? $214 = 3 · 71 + 1$
$71 = 3 · 23 + 2$
$ 23 = 3 · 7 + 2 $
$7 = 3 · 2 + 1 $
$2 = 3 · 0 + 2$
As a result, to obtain a base $3$ expansion of $214$, we take the remainders of divisions and we get that $(214)_{10} = (21221)_3$.
Question: why do the remainders give base $3$ expansion of $214$? And why order is from bottom to top?

$$214=(((((((2\times 3)+1)\times 3)+2)\times 3)+2)\times 3)+1$$
