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

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Solution

If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5

Prime factorisation of 6ⁿ= (2 ×3)ⁿ

It can be observed that 5 is not in the prime factorisation of 6ⁿ.

Hence, for any value of n, 6ⁿ will not be divisible by 5.

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

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