Question

show that 4n can never end with the digit zero for any natural number

Answer 1

For a digit to end with 0 it should have both 2 and 5 as a factor.

After factorizing 4 you get 4= 2*2
                                            =2^2
Therefore 4^n= 2^2*n

It only has 2 as a factor and 5 is missing.
Hence any number of the form 4^n (where n is any natural number) cannot end with the digit zero.

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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 .