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

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

Prime factorization of 6n= (2 × 3)^n

Therefore, the prime factorization of 6^ndoesn’t contain 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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