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Question
Check whether 6n can end with the digit 0 for any natural number n.
Solution
We know that
62 = (2 × 3)n
62 = 2n × 3n
i.e., In the prime factorisation of 6n, there is no factor 5.
The fundamental theorem of arithmetic states that any composite number may be written as a product of primes. This factorization is unique, regardless of the sequence in which the primes occur.
∴ Our assumption that 6n ends with digit 0, is wrong.
Thus, there does not exist any natural number n for which 6n ends with zero.
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