The criterion of divisibility by 11 needs organization and greater understanding of the process that must be carried out in order to know the divisibility of a number by 11.
The multiples of 11 quickly extrapolate the hundreds places, so we might come across numbers that have multiple digits, however with the verification process of divisibility by 11, it will seek a means that uses a smaller amount of digits for this verification.
"A number is divisible by 11, if the sum of the even-order digits subtracted from the sum of the odd-order digits results in a number divisible by 11. If the result is equal to 0, it can also be said that it is divisible by 11.”
We must understand what is said as even order and odd order, as confusion can arise that what should be done is “add the even numbers and add the odd numbers”, but that is not what is required. Even order and odd order refers to the order of the digits of the number, starting from left to right. Let's make a table with the order of the digits of the number: 2376.
As we saw in the divisibility criterion, we must add the digits that correspond to the odd order, and subtract from the sum of the digits of the even order. Let's do this process:
Subtract the sum of the even order digits by the sum of the odd order digits. If the result is negative, invert this subtraction to: (Sum of the odd order digits subtracted by the sum of the even order digits). In this situation we don't care what signal we get, we just want to check if this result is in fact divisible by 11.
As seen earlier, if the result is zero, we can say that the number being checked for divisibility by 11 is in fact divisible by the number 11, that is, 2376is divisible by 11.
Let's take another example. Verify the number 12574is divisible by 11.
As it is not possible to divide 1 by 11, we have that the number 12574 is not divisible by 11.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Kids School Team
