The rule to determine if a number is divisible by nine without using any division. Simply add up all the digits of the number. Repeat this until you come out with a one digit number. If this number is nine, the original number is divisible by nine.

9 * 98765 (yeah, I'm lazy) = 888885

8 + 8 + 8 + 8 + 8 + 5 = 45

4 + 5 = 9

8 * 36547 = 292376

2 + 9 + 2 + 3 +7 +6 = 29

2 + 9 = 11

1 + 1 = 2

I learned this back in the day from watching Square One on PBS.

On the show it had a little ditty that went along with it:

Nine, nine, nine,

Fantastic number nine.

Perfectly efficient,

It works out every time.

Nine, nine . . .

I can't believe I still remember that.

This trick is similar to how to find out if ANY number is divisible by eleven.