#### Question

Consider the number 6^{n} where n is a natural number. Check whether there is any value of n ∈ N for which 6^{n} is divisible by 7.

#### Solution

Since, 6 = 2 x 3; 6^{n} = 2^{n} x 3^{n}

⇒ The prime factorisation of given number 6^{n}

⇒ **6 ^{n} is not divisible by 7**.

Is there an error in this question or solution?

Solution Consider the number 6^n where n is a natural number. Check whether there is any value of n ∈ N for which 6^n is divisible by 7. Concept: Fundamental Theorem of Arithmetic.