Divisibility by 2, 3 and 9

When solving arithmetic problems like those in the NumberWiz app, it's good to check the divisibility of the result. It's trivial to find out if a number is divisible by 2: the last digit is even. 
It's also easy to find out if a number is divisible by 3: add the digits and see if the result is divisible by 3. If the result is too big, just add the digits of the result and see if the new result is divisible by 3. Example 1,375,896. 1+3+7+5+8+9+6 = 39. Too big, ok continue: 3+9=12. Still too big, ok continue: 1+2=3. Divisible by 3. The calculator says 1,375,896 = 458,632 x 3.
Try it for smaller numbers that you know from everyday life. 27: 2+7=9. Divisible by 3. 99: 9+9=18. 1+8=9. Divisible by 3. 34: 3+4=7. Not divisible by 3. 13: 1+3=4. Not divisible by 3.
Same rule applies to divisibility by 9. Example: 470,761,587. 4+7+0+7+6+1+5+8+7=45. Too big, ok continue: 4+5=9. Divisible by 9. The calculator says 470,761,587 = 52,306,843 x 9.
Really simple and useful rules of arithmetic. I'll go through other rules later. I'm particularly fond of the rules for 3 and 9, because they're so simple. What's more: every second number is divisible by 2 and every 3rd number is divisible by 3. This makes the rules even more useful!