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Question:

Check whether can end with the digit 0 for any natural number n.

Answer:

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

**We know that the factors for 6 = 2 x 3**

** So, ** ** 6 ^{n }= 2^{n} x 3^{n}**

**Thereby putting values like positive natural numbers in n = 1, 2, 3….. n but to get a 0 at the end the number has to be either multiplied by 0 or by 5. **

**Otherwise, the value of 2 ^{n} **

**and 3**

^{n}**will never end with 0. The unit value of 2**

^{n}**will always be even number except for zero and unit value of 3**

^{n}**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 equal to zero.**

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