Determining divisibility of number by 11 for large numbers

I’m looking for a way to determine a large number is divisible by 11

My understanding: (sum of digits at even positions – sum of digits at odd positions) % 11 == 0 ==> yes

This works for some examples.

Example: 3816 => (3+1) – (8+6) = -10
In case of negative, do we need to consider 2’s complement of -10 for modulo % with 11?

Similarly: 391679 => 11 – 24 = -13 (this number is also divisible by 11)

Could you please help me understand this? thanks in advance.

Answer

The numbers 3816 and 391679 are not divisible by 11. Just validating the difference between the sum of alternate digits with %(modulo) 11 is enough to check divisibility by 11, even if the difference is negative.