All natural numbers(composite or prime) have divisibility conditions. Let us derive some with some interesting ideas.
Div. Condition : Difference of the the sum of alternately placed digits is either zero or an integer multiple of 11.
if n is even.
if n is odd.
If n is even ,
If n is odd ,
Take any random natural number X . Let its digits be
can also be written as –
but we know that
Hence if X is divisible by 11 , it should divide the difference of the sum of odd and even placed terms.Hence proved.
Case 2 : n is odd
Proceede similar to Case 1.
Take a random integer X with digits
Case 1 : n – even