Question

Check whether 4n where n is a natural number can end with zero for any natural number n

Answer 1

4n can never end with the digit 0 for any natural number n because for a number to end with zero it shoul be divisible by 10 and therefore its factors should be 5 and 2.

But as 4 has only 2 as its factor, increasing its power will not make 5 as its factor. 

Thus it can never end with 0.

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 .