Question

Check whether 4 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

Answer:

Hence proved that for any natural number n, the value $4^n$ cannot ends with the digit zero.

Solution:

A digit ending with zero must need to have 2 and 5 as factors or the number itself should have ended with the digit zero.

The factors of 4 = 2×2

$=2^2\\\therefore 4^n=2^{2n}$

It has only 2 as a factor and 5 is missing.

Hence we cannot get zero at end of the value $4^n$ .

Where n = any natural number starting from 1.