Question

CHECK WHETHER 6n CAN END WITH THE DIGIT 0 FOR ANY NATURAL NUMBER n

Answer 1

no it cannot end. bcoz for any no to end with 0 it should have factors of both 2 and 5. but here it cannot be expressed in the form of powers of 2 and 5. therefore it cannot end with 0

Answer 2

If the number 6n ends with the digit zero (0), then it should be divisible by 5, as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6n = (2×3)n

Therefore, the prime factorization of 6n doesn’t contain prime number 5.

Hence, it is clear that for any natural number n, 6n is not divisible by 5 and thus it proves that 6n cannot end with the digit 0 for any natural number n.