Divisibility of twelve

How do we find out if a whole number is divisible by twelve? A number is divisible by twelve if it is divisible by three and also divisible by four. To recap:

• A number is divisible by three if its digit sum is divisible by three (see the article Divisibility by three for more details).
• A number is divisible by four if its last two digits are divisible by four (see the article Divisibility by Four for details).

Let's try the procedure for example on the number 1176: The digit sum 1 + 1 + 7 + 6 of the number gives us the result 15, which is a number divisible by three. The last two digits are 76, and this is divisible by four (because 76 divided by 4 is 19). So the number 1176 is divisible by 12 (if we divide 1176 by 12, we get 98).

What about a number like 438? The sum of the digits 4 + 3 + 8 is again equal to 15 and so the number is divisible by three. But the last two digits are 38 and that is not divisible by four. So the number 438 is not divisible by 12.