Divisibility Test for a number

Take a number (dividend) you want to check whether it is divisible by another number (divisor).
Leave aside last 2 digits of dividend.
Divisibility test for number or Divisor	Multiply the remaining no. by	Calculation or Test
7	2	add multiplication to last 2 digits
13	4	subtract last 2 digits from multiplication
17	2	subtract last 2 digits from multiplication
19	5	add multiplication to last 2 digits
23	8	add multiplication to last 2 digits
29	13	add multiplication to last 2 digits
31	7	add multiplication to last 2 digits
37	11	subtract last 2 digits from multiplication
41	18	add multiplication to last 2 digits
43	14	add multiplication to last 2 digits
47	6	add multiplication to last 2 digits
53	6	subtract last 2 digits from multiplication
59	18	subtract last 2 digits from multiplication
61	22	subtract last 2 digits from multiplication
67	33	add multiplication to last 2 digits
71	29	add multiplication to last 2 digits
73	27	add multiplication to last 2 digits
79	21	add multiplication to last 2 digits
83	17	add multiplication to last 2 digits
89	11	add multiplication to last 2 digits
97	3	add multiplication to last 2 digits
If this number is completely divisible by divisor, then the number (under consideration) will be (completely) divisible by the divisor.
A number will be divisible by a composite number, if it is divisible by all it's prime factors.
Eg. A no. is divisible by 15 if it is divisible by 3 and 5.
All other number tests you know, right?