Whimsy Girl

I mean it when I say you never know what you’ll find in here

You probably learned this in school, but since I’m in algebra class (again – lets not go there)  I’ve found it useful to look these up again.

Plus, as a homeschooling mom, this kind of stuff is always useful.

Here are a few more tricks that I learned somewhere along the way for determining if a decimal integer is a multiple of:

1. Duh.  Of course it is.
2. Is the last digit even?  Another easy one.
3. Add up the digits in the number.  If the result is a multiple of 3, then so is the number.  If the sum of the digits is too big for you to know whether it’s a multiple of 3 or not, recurse.  Add up its digits and see if that’s a multiple of 3.
4. Take the number formed from the last two digits.  If that’s a multiple of 4, so is the number.  Why?  Because 100 is a multiple of 4.
5. Is the last digit a 0 or a 5?  Too easy.
6. Is the number a multiple of 2 and 3?
7. Double the last digit and subtract it from the number formed by the remaining digits.  If that result is a multiple of 7, so is the original number.  If you can’t tell, recurse.  For instance, take 357.  Double 7 to get 14, subtract that from 35 and you get 21.  Since 21 is a multiple of 7, so is 357.
8. Take the number formed from the last three digits.  If that’s a multiple of 8, so is the number — because 1000 is a multiple of 8.
9. Add up the digits in the number.  If the result is a multiple of 9, then so is the number.  Again, you can recurse if you’re not sure.  It’s no accident that this rule for 9 is the same as the rule for 3.
10. Does it end with a 0?  Now we’re back in elementary school.
11. Add up all the odd digits to get one number, then add up all the even digits to get a second number.  If the difference between them is a multiple of 11 (zero included), then so is the number.  If you think about it, this is really the “11 Times Trick” reversed.  Let’s take 26719 as an example.  2 + 7 + 9 = 18, 6 + 1 = 7, 18 – 7 = 11, so 26719 is a multiple of 11.
12. Is the number a multiple of 3 and 4?

Looking at this list, the relationship between 3, 6, and 9 is obvious — as is the relationship between 4 and 8.  The unique characteristics of 7 and 11 are intriguing, don’t you think?

and of course I copied that from someplace.. if I knew this stuff I would NOT be taking this class

Credit goes to GEEKSARESEXY