On Wednesday I explained how to determine if a number is divisible by 3, 6, and/or 9. I also posted a comment with a link to rules for 2, 3, 4, 5, 6, 7, 8, 9, and 10. Therefore, I think it is time for 11 and 12.
Divisibility Rule for 11
Let’s say that we want to determine if 31823 is evenly divisible by 11. I will know that it is evenly divisible by 11 if
Let’s try 9123:
Let’s try one more together to make sure you understand the pattern. Is 9876543210 divisible by 11? Since
Okay, so now that we understand the pattern, how do we find a nearby number that is divisible by 11? Believe it or not, you just have to subtract the number that you get from our math problem to the original number, to get one that is divisible by 11.
Let’s use 9123.
Now let’s try our other number that wasn’t divisible by 11: 9876543210. We will subtract
Divisibility Rule for 12
A number is divisible by 12 if it is divisible by both 3 and 4. The reason this is true is because
If you have trouble looking at a two digit number and figuring out if it is divisible by four, try the following:
- If the right-most digit is odd, it is not divisible by four.
- If the right-most digit is 0, 4, or 8, the next digit to the left must be even.
- If the right-most digit is 2, or 6, the next digit to the left must be odd.
As I explained in my previous divisibility post, a number is evenly divisible by 3 only if the sum of the digits in the entire number is even divisible by three.