Divisibility by 2, 3 and 5 would be the most useful, as they would be applicable to an extremely wide range of numbers.
Work Step by Step
Divisibility by 2: If the number ends in an even digit (0, 2, 4, 6, 8), then it is an even number. This rule alone already identifies half of all numbers as being divisible by 2, hence it would be quite useful. Divisibility by 3: If the digit sum of the number is divisible by 3, the number itself will also be divisible by 3. Divisibility by 5: If the number ends in a 5 or 0, it is divisible by 5. This rule is extremely easy to remember!