How to find signs of divisibility in the n-ary number system?

Question

Mathematics

There is a number in the 18th number system.
It is necessary to determine whether it is divisible by 51:
A30B7834A10A16
As I understand it, here you can do something with division by 17 and by 3. But I don’t understand what.

Answer 1

What is easier:

• by 3 - the last digit must be divisible by 3
  
• by 17 - the sum of the digits must be divisible by 17