Question

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Check whether 4n can be end with digit zero where 'n' is natural number

Answer 1

if The number 4n, for any value of n were to end with digit zero then it would be divisible by 5. that is the prime factorization of 4n would contain the prime 5. this is not possible because 4n=(2)2n; so the only prime in the factorization of 4n is2. so the uniqueness of the fundamental theorem of arithmetic guarantees that there is no natural number n

for which 4n ends with digit zero.

Answer 2

Step-by-step 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 .