How do you tell if a number can be divided by 7? Check out this "divisibility graph" from David Wilson writing at Tanya Khovanova's Math Blog.
This method ends up working out kind of like a kids board game like "Chutes and Ladders" where you go 2 steps forward and then 3 back.
Here's the quick directions:
- Break your number down into digits.
- Start at the red zero. Go counterclockwise as many red dots as the leftmost digit of your number of interest.
- Follow the arrow to another red dot.
- Repeat steps 2 and 3 for all the remaining digits.
- For the last digit, skip step 3. The number in the red dot is your remainder.
For example, if you want to find out if 234 is divisible by 7, you start at 0, then go to 2 (for the first digit), and then follow the arrow to 6. Now go 3 more dots back to 2, and the follow the arrow to 6 again. Lastly, go 4 dots around to 3, and skip the last jump. So your remainder is 3. You can confirm this with long division: 234 divided by 7 is 33r3.
If you follow the pointers from Art DuPre in the comments, it turns out you can do this for any number. I did it for 13 without any trouble, and the programmed the method without a diagram into Excel. Cool.