determine all possible digits to fill in the blanks to make each of the following true:

a. 63 is a factor of _543

There are no digits that make the proposition true.

Step-by-step explanation:

63 = 9 x 7.

Therefore we're looking for a number which is a multiple of 9 AND a multiple of 7.

To know if a number is divisible by 9, the sum of its digits has to be either 9 or a multiple of 9.

So, we're going to sum up the digits we have so far: 5 + 4 + 3 = 12, the only digit that would give us a sum that's a multiple of 9 is 6 (because the sum would be 18). The number then would be 6543.

But this number is not a multiple of 7: 6543/7 = 934.71 and therefore it's not a multiple of 63.

Therefore, there are no digits to which the number _543 is a multiple of 63.