Question

Prove that 4n cannot end with zero.​

Answer 1

Answer:

4n cannot end with zero because it doesn't have both 2 and 5 as it's prime factors. However it has 2 as its one of the prime factors but to make it end with zero then it needs both 2 and 5 as it's prime factors.

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 .