Characteristics divisible by 2,3,5,7,9,11,13,4,25?

Characteristics divisible by 2,3,5,7,9,11,13,4,25?

2: The end is 0, 2, 4, 6, 8
3: The sum of all digits is a multiple of 3 (for example, 123 is 1 + 2 + 3 = 6, 6 is a multiple of 3, so 123 can be divided by 3
5: The end is 0,5
7 [13]: subtracting the last three digits from the front is a multiple of 7 [13] [for example, 1050050-1 = 49, 49 is a multiple of 7, so 1050 can be divided by 7]
9: The same three, just add up to a multiple of 9
11: Adding and subtracting numbers on odd [even] digits adding (greatly reducing) numbers on odd [even] digits is a multiple of 11 [for example: 121,1 + 1 = 2.2-2 = 0,0 can be divided by 11, so 121 can be divided by 11]
4,25: the last two digits can be divided by 4 [25]