Question

Consider the numbers 6n, where n is a natural number. Check whether there is any value of n for which 6n ends with the digit zero.

Answer 1

Answer:

                No

Step-by-step explanation:

To find whether the number 6ⁿ   ends with a digit 0 for any natural number 'n' we first find the factorization of the value 6ⁿ  .

Now we know that the factors for 6 = 2×3

Putting  6ⁿ ,  we get 6ⁿ = 2ⁿ×3ⁿ

Thereby putting values like positive natural numbers in n = 1, 2, 3….. n to get  0 at the end, the number has to be either multiplied by 0 or by 5, now the value of 2ⁿ will never end with 0 and the value of 3ⁿ can never end with 0 as well. The unit value of  will always be even number except zero and unit value of  3ⁿ will be 3, 9, 7, 1 thereby multiplying both factors will never have zero at the unit place of a number.

Therefore, there is no value of n that will give unit digit of 6ⁿ   equal to zero.

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