If the Avis identification number a1 a2 a11 8 has check digi

If the Avis identification number a_1 a_2 ...a_11 8 has check digit 5, what is the check digit for the Avis idenfication number a_1a_2 ... a_11 6?

Solution

the solution to the problem is simple , it is saying that first 11 digits of a number is same , but last digit of the two numbers is8,6

also first 11 digits 8 modulo (some number) and doing some operation on the number is =5

then 11 digits 6 modulo (same number) and doing same operation on the number is =?

let the some number be = 7

then 7 modulo 8 = 1 and 1 +4 =5

then 7 modulo 6 = 6 and 6+4 = 10

so 10 is the chek digit