Ways to test for divisibility by single-digit numbers in

base 10:

**1** - This is here for completeness. Every integer is divisible by 1.
**2** - The last digit is 0, 2, 4, 6, or 8.
**3** - The sum of the digits is divisible by 3. (If you are dealing with a freaking huge number you can apply this recursively.)
**4** - The last two digits form a number which is itself divisible by 4.
**5** - The last digit is 0 or 5.
**6** - The sum of the digits is divisible by 3
*and* the last digit is 0, 2, 4, 6, or 8.
**7** - I defer to how to determine whether a number is divisible by 7.
**8** - Either:
- The hundreds place is even, and the last two digits form a number which is divisible by 8.
**or**The hundreds place is odd, and the last two digits minus 4 form a number which is divisible by 8.

**9** - The sum of the digits is divisible by 9.

Divisibility is not symmetric. a | b usually doesn't imply b | a. The property that a | a means that divisibility is

**reflexive**.