 Hello and welcome to the session at a discovery following problem today. Check whether 6 to the power n can end with a digit 0 for any natural number n. Now let us write our solution. If the numbers 6n were to end with the digit 0, then it would be divisible by 5. The factorization would contain which is not possible because 6 to the power n is equal to 3 into 2 to the power n which can be written as 3 to the power n into 2 to the power n. So, the factorization are and we have no 5. Therefore, uniqueness of the fundamental theorem of guarantees factorization of 6 to the power n to a number for which 6 to the power n ends with the digit 0. We understood this problem by another nice day.