__Divisibility by 3, 6 or 9__

Have a large-ish number and need to know whether you can divide it by one of the above numbers? Easy. Just add up the digits. If the result is divisible by 3 (or 9), then so is the original number. If it's divisible by 9, it's automatically divisible by 3. If it's divisible by 3

*and*is even, then it's divisible by 6.

Example: 4,374

4 + 3 + 7 + 4 = 18

18 is divisible by both 3 and 9, so 4,374 is divisible by both. Since it's even, it's also divisible by 6. Go ahead and check it while I try a larger number.

Example: 5,660,193

5 + 6 + 6 + 0 + 1 + 9 + 3 = 30

30 is divisible by 3, but not 9. The original number is odd, so it's only divisible by 3 (not 9 or 6).

__Multiplying by 11__

We all know that multiplying a single-digit number by 11 is easy—just repeat the number. 11 times 7 is 77, 11 times 3 is 33, etc. Multiplying by larger numbers is pretty easy, too.

The first and last digits stay the same. For the middle number(s), add adjacent numbers together.

Example: 11 × 35 = 3_5.

Since 3 + 5 = 8, that's the middle digit.

So 11 × 35 = 385.

Bigger Example: 11 × 724 = 7_ _4.

7 + 2 = 9, and 2 + 4 = 6.

So 11 × 724 = 7,964.

What if one of those middle number sums results in a 2-digit number? Still works, you'll just have to do a little carrying over to the next column to the left.

Example: 11 × 3852 = 3_ _ _2

3 + 8 = 11. Oops, carry that 1 over to the left, so the first digit is 4.

8 + 5 = 13. Oops again. Carry that 1 to the 1 in the 11 above. (Confusing, yeah.) Second digit is 2, third is 3.

5 + 2 = 7. Okay, nothing fancy here.

So 11 × 3,852 = 42,372.

Now go and impress your non-mathematical friends.

## 2 comments:

hee. cool! thx for the 11 trick!

Anytime, S.Q. :-D

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