Question

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

Answer 1

$\huge\boxed{ANSWER}$

given,

6^n

if 6^n is to be end with for a natural number n it should be divisible by 2 & 5

prime factorisation of 6^n should contain the prime numbers 2 & 5 but 6^n contains only both in its prime factorisation...

[6^n=(2×3)^n)

since 5 is not present in the prime factorisation there is no natural number "n"for which 6^n ends with digit 0.

Answer 2

$Your\:Solution$

If any digit has last digit 10

That means It is divisible by 10

And the factors of 10 = 2 x 5

So, value 6n should be divisible by 2

and 5 both 6n is divisible by 2

But not divisible by 5

So ,it can not end with 0.