divisibility criterion for integer numbers using congruences

Question

let be a positive integer written in the form

$$ \sum_{n=0}^{k}a(n)10^{n} $$

my question is how can i deduce using mathematics if the number is divisible by 2 , 4 or another higher integer using congruences or another math theorem?

here $a(n)=0,1,2,3,4,5,6,7,8,9 $ for every 'n'

for example we know that a number can be divided by 2 if it ends in 2, it can be divided by 3 if the sum of its ciphers can be divided by 3 and so on

Answer 1

Since your writing is the usual base 10 form of a number you should check the usual divisibility rules:

https://en.wikipedia.org/wiki/Divisibility_rule