Question

Consider the number 4n², where n is a natural number. Check whether there is any value of n for which 4n ends with the zero.

Answer 1

Answer:

no, any value of n can never end with zero

Step-by-step explanation:

proof:  4=2*2

          therefore 4n=2*2

           but any number ends with zero has a factors of 2 and 5

           here it is 2*2

hence for any value of power n it does not end with zero

hence proved

hope it helps

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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 .