# Check whether $$6^n$$ can end with the digit 0 or any n $$\in$$ N.

## Solution :

If the number $$6^n$$ ends with the digit zero. Then it is divisible by 5.

Therefore, the prime factors of $$6^n$$ contains the prime number 5. This is not possible because the only primes in the factors of $$6^n$$ are 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other prime in the factors of $$6^n$$.

So, there is no value of n in natural numbers for which $$6^n$$ ends with the digit zero.