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

Q5  Check whether 6 ^n  can end with the digit 0 for any natural number n.

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S Sayak

By prime factorizing we have

6n = 2n x 3n

A number will end with 0 if it has at least 1 as the power of both 2 and 5 in its prime factorization. Since the power of 5 is 0 in the prime factorization of 6n we can conclude that for no value of n 6n will end with the digit 0.

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