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Question

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

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Solution

If 6n is end with zero for a natural number n, it should be divisible by 2 and 5.
This means that prime factorization of 6n should contain the prime number 2 and 5.
But it is not possible because 6n=2n×3n so 2 & 3 is only prime in the factorization of 6n.
Since 5 is not present in the prime factorization, there is no natural number n for which 6n ends with the digit zero.


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