Question

Consider the number $4^n$, where $n$ is a natural number. Check whether there is any value of $n\in N$ for which $4^n$ ends with the digit zero.

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is B No

For the number $4^n$ to end with digit zero for any natural number n, it should be divisible by $5$. This means that the prime factorisation of $4^n$ should contain the prime number $5$.But it is not possible because $4^n=(2{)}^{2n}$ so $2$ is the only prime in the factorisation of $4^n$. Since $5$ is not present in the prime factorization, so there is no natural number $n$ for which $4^n$ ends with the digit zero.