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

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#### Solution

if the number 6^{n} ends with the digital zero, then it is divisible by 5. Therefore the prime factorization of 6^{n} contains the prime 5. This is not possible because the only prime in the factorisation of 6^{n} is 2 and 3 the uniqueness of the fundamental theorem of arithematic guarantees that these are no other prime in the factorization of 6^{n}.

Hence it is very clear that thereis novalue of n in natural numbers for which 6^{n} ends with the digit zero.

Concept: Fundamental Theorem of Arithmetic

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