Question

check whether 3n can end with the digit 0 for any natural number n

Answer 1

If the 3n , for any n, were to end with the digit zero, then it would be divisible by 2&5.that the prime factorisation of 3n would contain the primes 2 &5.That is not possible because prime factorisation of 3n doesn't contain 2&5. By uniqueness of fundamental theorem of arithmetic guarantees that 3n will never end with zero

Answer 2

Answer:

3^n cannot end with 0 for any natural number .

Step-by-step explanation:

we know that for any number n in 3^n ,it has to end with 5 or 10 or by any multiple of 10 which ends with zero . if 3^n ends with zero it should be divisible by 5 .

we also know that any number divided by 5 if it has 0 or 5 on units place .

prime factorization of 3^n is (3×1)^n .

here prime factorization of 3^n doesn't contain prime number 5 .

hence , it is obvious that for any number n , 3^n is not divisible by 5 .

thus,it prove that 3^n cannot end with digit 0 for natural number n