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

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

Solution:  Given : 6ⁿ

To find: Whether 6ⁿ end with 0 or not.

We know that any number which is multiplied by 5 or 10, or multiples of 10 end with 0.

Let 6ⁿ can end with the digit 0. Then 5 must be a prime factor of it.

Now, 6ⁿ = (2 × 3)ⁿ, i.e., 2 and 3 are the only prime factors, which is a contradiction to the fact that 5 is a prime factor of 6ⁿ.

Hence our assumption is wrong.

Therefore, 6ⁿ can not end with the digit 0 for any natural number n.

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