Question

check whether 4^n ncan end with 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 =22n; 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.

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