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Check whether 6^n can end with the digit 0 for any natural number n.

  

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Check whether 6n can end with the digit 0 for any natural number n.

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If the number 6n ends with the digit zero (0), then it should be divisible by 5, as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6n = (2×3)n

Therefore, the prime factorization of 6n doesn’t contain prime number 5.

Hence, it is clear that for any natural number n,6n is not divisible by 5 and thus it proves that 6n cannot end with the digit 0 for any natural number n.

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