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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

If the number 6^nends 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 6^n= (2×3)^n
Therefore, the prime factorization of 6ndoesn’tcontain prime number 5.
Hence, it is clear that for any natural number n,6nis not divisible by 5 and thus it proves that 6^ncannot end with the digit 0 for any natural number n.

​Thanks

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