Question

Check whether 6^n ( 6 to the power n) ends with digit zero

Answer 1

Step-by-step explanation:

To check :-

• 6^n ends with digit zero

If the number 6^n, for any n, were to end with the digit zero, then it would be divisible by 5. That is the prime factorisation of 6^n would contain the prime number 5. This is not possible because 6^n = (2×3)^n, so the only prime in the factorisation of 6^n is 2 and 3 not 5. And it is necessary that the number which ends with zero divisible by 5. But 6^n this isn't divisible by 5. So, 6^n can't end with the digit zero(0).

Answer 2

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If the number 6ⁿ ends with zero, then it would be divisible by 5.

If it ends with zero then its prime factorisation should contain 5 in it.

The Prime factorisation of 6ⁿ is 2(3ⁿ).

Therefore, the prime factorisation of 6ⁿ does not contain 5 in it.

So, there is no natural number for which 6ⁿ ends with zero.

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