If a number is divisible both by 2 and 3, then it is divisible by 12.

If a number divides three numbers exactly, it must divide their sum exactly.

If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.

A number with three or more digits is divisible by 6, if the number formed by its last two digits (i.e., ones and tens) is divisible by 6.

A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.