Question

check whether 6n can end with the digit 0for any natural number n ​

Answer 1

Answer:

If $6^{n}$ were to end with digit zero, for any natural number n, then it will contain the prime factor prime 5. This is not possible because $6^{n}$ can be written as     $(2$ × $3)^{n}$.

So, the only primes in the factorization of  $6^{n}$ are 2 and 3. Therefore, by the uniqueness of fundamental theorem of arithmatic there are no other primes in the factorization of  $6^{n}$. so, there is no natural number n for which  $6^{n}$ ends with digit zero.

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