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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. - Mathematics

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Sum

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.

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Solution

Since, 6 = 2 x 3; 6n = 2n x 3n

⇒ The prime factorisation of given number 6n

6n is not divisible by 7.

 

Concept: Fundamental Theorem of Arithmetic
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