Question

Prove that 2^n cannot be a positive integer which ends with digit 0 for any natural number n.

Answer 1

AnswEr:

If the number $\sf\:2_n$ ends with digit zero, then it should be divisible by 5.

We know that, Any Number with unit place as 5 and 0 is divisible by 5.

$\rule{200}2$

Now,

$\dag$ Prime Factorisation of number $\sf\:2_n = (2 \times\; 1)^n$

Here we can see that the prime Factorisation of the number $\sf\:2_n$ doesn't contains 5 as a prime Number.

$\rule{200}2$

Now we can say that for any natural number n, the number $\sf\:2_n$ is not divisible by 5.

Thus, $\sf\:2_n$ cannot end with the Digit zero (0) for any Natural number n.

Answer 2

$\huge\underline\mathfrak\blue{Answer⤵}$

Refer the provided attachment

Hope it helps..

Keep smiling..☺

_____❤_____