Check whether 4^n can end with the digit 0 for any natural number a.

Question

Check whether 4ⁿ can end with the digit 0 for any natural number n.

Answer 1

If the number 4ⁿ for any n, were to end with the digit Zero then it would be divisible by 5 and 2.that is prime factorization of 4ⁿ would contain the prime 5 and 2. This is not possible beacuse 4n =(2)²ⁿ; so the only prime in the  factorization of 4ⁿ is 2. So, the uniqueness of the Fundamental Theorem of Arthmetic guarantees that there are no other primes in the factorization of 4ⁿ . So, there is no natural number n for which 4ⁿ ends with the digit zero.