Question

Show that 8n cannot end with the digit zero for any natural number n
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Answer 1

Answer:

If it is 8n then it can end with 0 but if it is 8ⁿ then it can't end with 0.

For a number to end with the digit 0 it's prime factorisation should have 2 and 5 as a common factor.

here 8ⁿ = (2*4)ⁿ doesn't have 5 in its prime factorisation.

Therefore 8ⁿ cannot end with the digit 0.

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Answer 2

Answer:

your answer is here

Step-by-step explanation:

We know 8n = (2 to the power 3)n = 2 to the power 3 n

If 8n end with zero then 10 is factor of 8n.

8n = 2 to the power 3n = (5)(2)

5 is factor of 2, which is a contradiction

So, our assumption is wrong. Hence  8n cannot end with zero