Question

check whether 8 end with the digit zero for any natural number n​

Answer 1

Answer:

Solution:-

If the number "8^n", for any natural number "n", is to end with digit 0, then it would be divisible by 2 and 5. This is not possible because

So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there is no other prime accept "2" in the factorisation of "8^n" .

So, there is no natural number "n" for which "8^n" ends with digit "0".

Step-by-step explanation:

Answer 2

Answer:

Solution:-

If the number "8^n", for any natural number "n", is to end with digit 0, then it would be divisible by 2 and 5. This is not possible because

{8}^{n} = {( {2}^{3} )}^{n} = {(2 \times 2 \times 2)}^{n} .8

n

=(2

3

)

n

=(2×2×2)

n

.

So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there is no other prime accept "2" in the factorisation of "8^n" .

So, there is no natural number "n" for which "8^n" ends with digit "0".

I hope its helpful