All Your Base Are Belong To Us

If we have an integer in radix/base n, so the possible digit for that integer is between 0 - (n-1). Example: The number in decimal (10) is composed of a digit between 0 - 9, we won't see a number in base-7 have 7 as a digit.

So from the question, we can say that base of the number is at least greater than 6. Thanks

In integer base representations, the digits in base $b$ are $0 ~\text{to}~b-1$ . Since the number includes $6$ , the only possible base from the choices is $\boxed{7}$ .