Check whether 4^n can end with the digit 0 fo | vedclass

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Question

(B) For a number to end with the digit $0$,it must be divisible by $10$. This means its prime factorization must contain both $2$ and $5$ as factors.

Vedclass · Accepted Answer

No,it cannot end with $0$.

Vedclass · Answer

(B) For a number to end with the digit $0$,it must be divisible by $10$. This means its prime factorization must contain both $2$ and $5$ as factors. The prime factorization of $4^n$ is $(2^2)^n = 2^{2n}$. Since the only prime factor of $4^n$ is $2$,it does not contain $5$ as a factor. Therefore,$4^n$ can never end with the digit $0$ for any positive integer $n$.

Check whether $4^n$ can end with the digit $0$ for any positive integer $n$.

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