Question

Dear Mitch,

You mentioned recently that you would be giving more of the divisibility tests.  We really appreciated the one you posted for the number three, so do you think you could post another one or two this week?

Thank you,

Mr. Lablonski

Answer

Dear Mr. Lablonski,

Of course!

Since you mentioned the one I posted for the number three, the next logical one to post (because it is the only one that is based upon a similar premise) is the test to see if a large number is divisible by the number 9.

Just like the one for three, you can take a large number, such as 123,456,345,789,876,111, and add all the digits together.  If the sum you reach is divisible by 9, then so is the giant number from which you  started.

So: 1 + 2 + 3 + 4 + 5 + 6 + 3 + 4+ 5 + 7 + 8 + 9 + 8 + 7 + 6 + 1 + 1 + 1 =  81.

And since 81 is divisible by 9, that whole number (123,456,345,789,876,111) is indeed divisible by nine as well.

Note, although it is true that any number that is divisible by nine is also divisible by three, it does NOT neccessarily work the other way around.  Example:  12 is divisible by 3, but it is NOT divisible by 9.  That is important to remember!

Hope this helps,

Mitch