Question

ANSWER IT PLS FOR BRAINLIEST FOR SURE



Check whether 4n can be end with digit zero where 'n' is natural number

Answer 1

Answer:

4n cannot end with zero for any natural number n

Step-by-step explanation:

Lets take the example of a number which ends with zero

So,10 = 2ₓ5

100=2ₓ2ₓ5ₓ5

Here we note that numbers ending with 0 has both 2 and 5 as their prime factors.

Whereas 4ⁿ =2ₓ2

does not have 5 as a prime factor

So,it does not end with zero

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 .