Check whether 6^n can end with the digit 0 fo | vedclass

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Question

(B) For any number to end with the digit $0$,its prime factorization must contain the factors $2$ and $5$.The prime factorization of $6^n$ is $(2 	im

Vedclass · Accepted Answer

No,it cannot end with $0$.

Vedclass · Answer

(B) For any number to end with the digit $0$,its prime factorization must contain the factors $2$ and $5$.The prime factorization of $6^n$ is $(2 	imes 3)^n = 2^n 	imes 3^n$.Since the prime factorization of $6^n$ only contains $2$ and $3$,it does not contain the factor $5$.Therefore,by the Fundamental Theorem of Arithmetic,$6^n$ cannot end with the digit $0$ for any natural number $n$.

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

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