Check Whether 6ⁿ Can End with the Digit 0 for Any Natural Number n

Video Explanation

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Solution

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

Step 1: Understand the Condition for a Number to End with 0

A number ends with the digit 0 if and only if it is divisible by 10.

10 = 2 × 5

So, a number must have both factors 2 and 5 in its prime factorisation.

Step 2: Prime Factorisation of 6ⁿ

6 = 2 × 3

∴ 6ⁿ = (2 × 3)ⁿ = 2ⁿ × 3ⁿ

In this expression, there is no factor of 5.

Step 3: Conclusion

Since 6ⁿ does not contain the factor 5 for any natural number n, it cannot be divisible by 10.

Final Answer

∴ 6ⁿ can never end with the digit 0 for any natural number n.

Conclusion

Thus, because 6ⁿ lacks the factor 5 in its prime factorisation, it cannot end with the digit 0 for any value of n.