check whether 6 power n can end with the. digit 0 for any natural number n
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5
The answer is NO.
The answer lies in the prime factorisation of 6.
Here,
6 = 2•3
so,
6ⁿ = 2ⁿ•3ⁿ
But we know that for unit digit to be 0, the number itself must be a factor of 10 or 2•5.
And since, 6ⁿ does not have any 5 as its prime factors, so 6ⁿ cannot end with digit 0, for any n.
The answer lies in the prime factorisation of 6.
Here,
6 = 2•3
so,
6ⁿ = 2ⁿ•3ⁿ
But we know that for unit digit to be 0, the number itself must be a factor of 10 or 2•5.
And since, 6ⁿ does not have any 5 as its prime factors, so 6ⁿ cannot end with digit 0, for any n.
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Answered by
1
Let, 6^n be any given integer and n=any natural number
So, by the prime factorisation method we know that the only prime factors of 6 are 2&3.
But if 6^n ends with the digit 0 it must have 5 as one of it's factors.
Also, from the fundamental theory of arithmetic we know that the prime factorisation of any number is unique.
So, 6^n can never end with the digit 0.
So, by the prime factorisation method we know that the only prime factors of 6 are 2&3.
But if 6^n ends with the digit 0 it must have 5 as one of it's factors.
Also, from the fundamental theory of arithmetic we know that the prime factorisation of any number is unique.
So, 6^n can never end with the digit 0.
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