Divisibilty Tests

Numberphile: Why 7 is Weird,
Solving Seven

2: Even
3: Digitsum = 3m
4: Last 2 digits (∵100 = 4n)
兌成一百蚊紙看零頭
5: End 5, 0
6: Even, Divisible 3
7: 5x Last + Rest, or: Rest - double Last
(eg 483 = 48 + 3 × 5)
or 兌成一百找二蚊 (=98) 看零頭
8: Last 3 digits, chop off all 200n & 120
兌成二百蚊紙看零頭 (或再扣百二)
9: Digitsum = 9m
10: End 0
11: Alternating Sum 單雙位差 = 11m
12: Divisible 3, 4

* 7 的倍數 : 1, .. ,77, 84, 91, 98
* 11: or 兌成一百找一蚊 (=99) 看零頭

For more (up to 30), see Wikipedia: Divisibility rule.