Will a number divide by 11, 7 or 13?

Here are three little tricks which could save you a lot of grief
if you're a tough person who doesn't use calculators.

The 11 test      The 7 test      The 13 test  

Will a number divide by 11?

There's a quick way to know if a number will divide exactly by 11 with no remainder - and not many people know it!

What you do:

Let's try one...91825074 Yuk! But will it divide by 11?

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!)

Will a number divide by 7?

On page 111 of "Murderous Maths" you'll find a the long way of testing if a number will divide by 7. However since the book came out, we've found a slightly quicker way!

We'll try 161623 Well, there's no point in just testing a little number is there?

If your number has three or more digits, you could also try this brilliant "7 test" that was sent to us by a Murderous Maths fan in Kent called Jaimie Oldham.

Try 2723

When you do any "7" tests, it's handy to remember that 77, 84, 91 and 98 all divide by 7.

Will a number divide by 13?

This is similar to seeing if a number will divide by 7.

We'll try 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

Back to The Mean And Vulgar Bits

The Prime Counter

Murderous Maths Main Index Page