Question

Show that any number of the form 4n,n€
N can never end with the digit 0

Answer 1

Step-by-step explanation:

Any number of the form 4n will be zero if it's factor is 5 and 2

Now. 4n=`2²ñ

But , here only 2 is the factor of 4n

that's why

any number of the form 4n,4€ can never end with the digit 0

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 .