Check whether 4ⁿ can end with the digit 0 for any natural number n.

If 4ⁿ is divisible by 10 then it can end with digit zero

If it is divisible by 10 it has to be divisible by 5 and 2 both

The prime factorization of 14 is 2 × 2 which is 2²

⇒ 4ⁿ = (2²)ⁿ = 2²ⁿ

Observe that 2²ⁿ is divisible by 2 (because and 2^2n–1 is intan eger for n≥1) but not by 5 because there is no 5 in prithe me factorization of 4

Hence 4ⁿ is not divisible by 10

Hence 4^{n ee}doesnot end with 0 for any natural number n