Here are three little tricks which could save you a lot of grief

if you're a tough person who doesn't use calculators.

- Put (or imagine) alternate + and - signs in front of the digits
- Total them all up
- If the total is zero, or if the total divides exactly by 11, then the original number will divide by 11.

- Put the signs in: +9 -1 +8 -2 +5 -0 +7 -4
- Get all the "+" bits and "-" bits together if you like: +9 +8 +5 +7 - 1 -2 -0 -4

This becomes: 29 - 7 = 22 - 22 divides by 11, so that means 91825074 will divide by 11 too!

If you try 17483103

You get +1 -7 +4 -8 +3 -1 +0 -3 which makes -11. That still counts as dividing exactly by 11, so 17483103 divides by 11.

What use is all this?

If you get around to breaking massive numbers into prime factors (this comes up in "The Mean and Vulgar Bits") this trick can save a lot of time!

Another time this comes in handy is when you're the all supreme ruler of a massive planet and the entire population wants to know if they can all be divided neatly up into football teams.

The 11 TEST (With a pretty counter!)

- Take off the last digit and multiply it by 2
- Subtract it from the digits you have left.
- If the answer divides by 7 (or is zero), then your original number will also divide by 7!

- Take off the last digit and x 2, so we get 3 x 2 = 6
- Subtract this from the other digits so we get 16162 - 6 = 16156. But does this divide by 7?
- Do it again! We get 1615 - (6 x 2) = 1615 - 12 = 1603. Does this divide by 7?
- On we go... 160 - 6 = 154
- ...and on... 15 - 8 = 7 YES! 7 divides by 7, so 161623 also divides by 7!

- Take off the last two digits then multiply the other digits by 2.
- Add your answer to the two digits you took off.
- If the answer divides by 7 then your original number will also divide by 7!

- Take off the last two digits to leave 27 and then 27 x 2 = 54
- Add your answer to the two digits you took off: 54 + 23 = 77.
- As 77 does divide by 7 then so does 2723.

- Take off the last digit and multiply it by 9
- Subtract it from the digits you have left.
- If the answer divides by 13 (or is zero), then your original number will also divide by 13!

- Take off the last digit and x 9, so we get 2 x 9 = 18
- Subtract this from the other digits so we get 22408 - 18 = 22390. But does this divide by 13?
- A BIT OF EXCITEMENT! As the last digit is "0" we can just knock it off and continue testing. So does 2239 divide by 13?
- We get 223 - (9 x 9) = 223 - 81 = 142. Does this divide by 13?
- On we go... 14 - 18 = -4. -4 does not divide exactly by 13, so neither does 224082.

However, if we'd started with 224081 the sums would have been...

22408 -9 =22399 then 2239 -81= 2158 then 215 -72= 143 and finally 14 -27= -13

... and as -13 * does* divide
exactly by 13, therefore 224081 divides by 13 too!

Back to the Original Murderous Maths Book