Question

check weather 4n
can end with digit zero from any natural number 'n'​

Answer 1

❒ We've to check whether the number 4n can end with digit 0 for any natural number n or not.

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀

Therefore,

⠀

If the number $\sf\:4_n$ ends with digit zero, then it should be divisible by 5.

⠀

As We know that,

⠀

• Any Number with unit place as 5 and 0 is divisible by 5.

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

⠀⠀⠀⠀

Now,

★ Prime Factorisation of number:

• $\sf\: 4_n = (4 \times\; 1)^n$

⠀

Here we can see that the prime Factorisation of the number $\sf\: 4_n$ doesn't contains 5 as a prime Number. Now we can say that for any natural number n, the number $\sf\: 4_n$ is not divisible by 5.

⠀

Thus, $\sf\: 4_n$ cannot end with the Digit zero (0) for any Natural number n.

Answer 2

Required solution -

~ We have to check weather 4n can end with digit zero from any natural number n.

Let's see what to do..!

~ As we already know that if any number end with digit zero then it is surely divisible by 2 and 5. Means to solve this type of questions it is necessary to learn rule of divisibility.

Henceforth, it's also cleared that 4n have it's factor as 2 and 5 for sure.

Considering, 4n as (2×2)n = 2²n

~ Now according to the fundamental arithmetic theorm 4n have it's factor only in the power of 2.

Henceforth, 4n can never be end with digit zero from any natural number 'n'