Question

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

Answer 1

for an number to end with zero, the number has to have factors of both 2 and 5.

we know that 6=2x3

6 has a factor of 2 but does not have a factor of 5.hence even though n can be equal to any number,6^n=/=a number ending with zero

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Answer 2

Answer:

$\large\boxed{\sf{NO}}$

Step-by-step explanation:

Let us assume that ${6}^{n}$ ends with digit 0, where n is a natural number.

Now, we know that, if any number ends with 0, it must be divisible by 5.

So, prime factorisation of ${6}^{n}$ should contain 5 as a prime factor.

Now, lets find out prime factors.

$=> {6}^{n} = {(2\times 3)}^{n} = {2}^{n}\times {3}^{n}$

Clearly, it doesn't contain 5 as prime factor.

Therefore, our assumption is wrong.

Hence, ${6}^{n}$ can't end with 0.