Question

Check whether 4 to the power n can end with the digit 0 for any natural number n.​

Answer 1

Answer :-

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

Step-by-step explanation :-

→ 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 .

Answer 2

Step-by-step explanation:

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

here , 4ⁿ = ( 2² )ⁿ = 2²ⁿ .

→ hence 2 is the only prime factor of 4ⁿ .

and we also know that the prime factorisation of each number is unique .

Hence , 5 is not a factor of 4ⁿ