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.

Now,

Prime Factorisation of Number

$\implies\sf 2^n = (2 \times 1)^n$

$\rule{150}2$

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

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.

$\rule{150}2$

Answer 2

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$\huge \tt {Answer:}$

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If the number 2^n,ends with digit zero, then it must be divisible by 5 as we know,Any Number with unit place as 5 and 0 is divisible by 5.

Hence,

Prime Factorisation of Number

➠2^n = 2×1

Here we can see that the prime Factorisation of the number 2^n ,doesn't contains 5 as a prime Number.we can say that for any natural number n, the number 2^n2 is not divisible by 5.

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