Question

check whether 6n can end with the digits 0 for any natural number n
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Answer 1

Answer:

6ⁿ = (2×3)ⁿ

The primes in the factorisation of 6ⁿ are 2 and 3.

For 6ⁿ to end in digit 0, prime factorisation of 6ⁿ should contain the primes 2 as well as 5.

Therefore, there is no natural number n for which 6ⁿ ends with digit 0.

Answer 2

Answer:

(2×3)n

Step-by-step explanation:

If the number 6n ends with the digit zero (0), then it should be divisible by 5, as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6n = (2×3)n

Therefore, the prime factorization of 6n doesn’t contain prime number 5.

Hence, it is clear that for any natural number n, 6n is not divisible by 5 and thus it proves that 6n cannot end with the digit 0 for any natural number n.

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