Question

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Check whether 4n can end with the digit 0 for any natural number n



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Answer 1

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Check whether 4n can end with the digit 0 for any natural number n

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This is not possible beacuse 4n =22n; so the only prime in the factorization of 4n is 2. So the uniqueness of the Fundamental Theorem of Arthmetic guarantees that there are no other primes in the factorization of 4n . So there is no natural number n for which 4n ends with the digit zero.

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Answer 2

Step-by-step explanation:

It will not end with zero for any value of n.

4^n = 2^2n

Now, if a number ends with zero, it should be divisible by 5.

→ One of the prime factors will be 5. But 4^n is not divisible by 5, therefore it will never end with zero.