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Real Numbers

Question

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Consider the number 6ⁿ, where n is a natural number. Check whether there is any value of n ∊ N for which 6ⁿ is divisible by 7.

Solution

Since 6 = 2 × 3

6ⁿ = 2ⁿ × 3ⁿ

⇒ The prime factorisation of given number 6ⁿ does not contain the prime number 7.

⇒ 6ⁿ is not divisible by 7.

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