Question

show that any number of the form 4n, nEN can never end with the digit 0

Answer 1

here we have to take the no. which ends with 0.......then here we came to know that we want a pair of 2 and 5 if no. is ending with 0.....so by this way we can prove it...

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 .