Question

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

Answer 1

Answer:

4^n can not end with digit 0

Step-by-step explanation:

4^n

if n = 0

then 4^0 = 1

4^odd number ends with 4

4^(2n+1) ends with 4

4^1 = 4 ,

4^3 = 64  

4^5 = 1024

4^even number ends with  6

4^2n end with 6

4^2 = 16

4^4 = 256

4^6 =  4096

so 4^n can end with digit 1 , 4 or 6 only so

4^n can not end with digit 0

Answer 2

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 .

$\therefore$ So, 5 is not a factor of 4ⁿ .

Hence, 4ⁿ can never end with the digit 0 .