Question

For what value of n such that 4^n ends with digit 0

Answer 1

Answer:

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Step-by-step explanation:

If the number 4n , for any n, were to end with the digit zero, then it would be  divisible by 5. That is, the prime factorization of 4n  would contain the prime 5. This is  not possible because 4n = (2)2n  ; so the only prime in the factorization of 4n   is 2. So, the  uniqueness of the Fundamental Theorem of Arithmetic 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  ....