Divisibility by 12

How can we tell whether an integer is divisible by 12? A number is divisible by 12 if it is divisible by 3 and also divisible by 4. A quick reminder:

• A number is divisible by 3 if the sum of its digits is divisible by 3 (see the article on divisibility by 3 for more detail).
• A number is divisible by 4 if its last two digits form a number divisible by 4 (see the article on divisibility by 4 for more detail).

Let’s try the method on 1,176. The sum of the digits 1 + 1 + 7 + 6 is 15, which is divisible by 3. The last two digits make 76, which is divisible by 4 (because 76 ÷ 4 = 19). So 1,176 is divisible by 12 (dividing 1,176 by 12 gives 98).

And what about 438? The sum of the digits 4 + 3 + 8 is again 15, so the number is divisible by 3. But the last two digits make 38, which is not divisible by 4. So 438 is not divisible by 12.