Question

Show that 12n cannot end with the digit 0 or 5 for any natural numbern

Answer 1

For a number 12n for any natural number n to end with the digit zero it should have both 2 and 5 in it

i.e. the prime factorisation of 12n should both 5 and 2 as factors

but this is not possible since 12n = (2*3*2)n

therefore the only primes in the prime factorisation of 12n is 2 and 3

the fundamental theorem of arithmetics ensures that there are no other primes in the factorisation of 12n

hence for a number 12n with any number will not end with the digit zero or 5 since there is no 5 in its prime factorisaton