Question

Example 5 : Consider the numbers 4". where n is a natural number. Check whether
there is any value of n for which 4* ends with the digitaro​

Answer 1

Method - 1:

Let us take the example of a number which ends with digit 0

.

So, 10 = 2 × 5

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

Whereas, 4ⁿ = (2 × 2)ⁿ

It does not have 5 as their prime factor.So,it does not end with zero.

Therefore, 6ⁿ cannot end with zero for any natural number n.

Method - 2:

Prime factorization of 4ⁿ = (2 × 2)ⁿ

It can be observed that 5 is not in the prime factorization of of 4ⁿ.

Hence, there is no natural number n for which 4ⁿ ends with the digit zero.

Answer 2

Answer:

since prime factor of 4 is 2x2 which doesn't have any prime factorization of 2 and 5 together. So 4^n can never ends with zero for any natural number n.