Question

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

Answer 1

In order to check whether 6ⁿ can end with the digit 0 for any natural number n, let us find the factors of 6. 

It’s seen that the factors of 6 are 2 and 3. 

So, 6ⁿ = (2 x 3)ⁿ 

6ⁿ =2ⁿ x 3ⁿ 

Since, the prime factorization of 6 does not contain 5 and 2 as its factor, together. We can thus conclude that 6ⁿ can never end with the digit 0 for any natural number n.