Question

Show that any number of the form 4n nen can never end with the digit 0

Answer 1

Here Is Your Ans ⤵

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➡4^n can not end with the Digit Zero because in their prime factoraisation 5 is not contain

➡4^n = (2^2)^n

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Answer 2

Explanation:

→ No, 4ⁿ can never end with the digit 0 for any natural number n .

→ If 4ⁿ ends with 0 then it must have 5 as a factor .

But, 4ⁿ = ( 2² )ⁿ = 2²ⁿ .

→ It shows that 2 is the only prime factor of 4ⁿ .

Also, we know from the fundamental theorem of airthematic that the prime factorisation of each number is unique .

So, 5 is not a factor of 4ⁿ .

Hence, 4ⁿ can never end with the digit 0 .