Question

Q-8. Check whether 4^nwhere n is natural number, can end with degit 0 for any natural number n. ​

Answer 1

Answer:

No.

4^n can never end with digit zero, where n is any natural number.

Step-by-step explanation :

Here the number 'a' is 4^n , where n is any natural number.

By prime factorisation of 4 , we get

4 = 2 × 2 = 2^2

We know that, the number can end with zero if its prime factorisation has 2^m × 5^n . Here prime factorisation of 4 does not contain this form.

Thus 4^n cannot end with digit zero, for any natural number n.

Verification :

We can verify this by trial and error method.

CASE I -

Let n be 1 , then

4^n = 4^1 = 4

Here it does not end with digit zero.

CASE II -

Let n be 2 , then

4^n = 4^2 = 4 × 4 = 16

Here also it does not end with digit zero.

CASE III -

Let n be 3 , then

4^n = 4^3 = 4×4×4 = 64

Here also it does not end with digit zero.

CASE IV -

Let n be 4 , then

4^n = 4^4 = 4×4×4×4 = 16×16 = 256

Here also it does not end with digit zero.

CASE V -

Let n be 5, then

4^n = 4^5 = 4×4×4×4×4 = 16×16×4

= 1024

Here also it does not end with digit zero.

In any of the case mentioned above, we get that 4^n can never end with digit zero, where n is any natural number.

Hence, 4^n can never end with digit zero, for any natural number n.