Question

Can 12ⁿ end with the digit 0 or 5 for any natural number ‘n’?

Answer 1

if 12^n end with 0 or 5 then its prime factorization will have 5 but we know that 12^n have only 2,3 as its prime factors and we know that prime factorization of a number is unique.
hence, 12^ n cannot end with 0.