Question

Show that 6^n can never end with digit 0 for any natural number n.​

Answer 1

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There is no natural number n for which 6ⁿ ends with the digit zero.

If 6ⁿ is to end with zero for a natural number n,

it should be divisible by 2 and 5.

This means that the prime factorisation of 6ⁿ should contain the prime number 5 and 2 .

But it is not possible because

6ⁿ = (2×3)ⁿ = 2ⁿ × 3ⁿ

Since , 5 is not present in the prime factorisation , there is no natural number n for which 6ⁿ ends with the digit zero.

Answer 2

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There is no natural number n for which 6ⁿ ends with the digit zero.

If 6ⁿ is to end with zero for a natural number n,

it should be divisible by 2 and 5.

This means that the prime factorisation of 6ⁿ should contain the prime number 5 and 2 .

But it is not possible because

6ⁿ = (2×3)ⁿ = 2ⁿ × 3ⁿ

Since , 5 is not present in the prime factorisation , there is no natural number n for which 6ⁿ ends with the digit zero.

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