The largest 4-digit number that can be formed using the digits 4, 0, 3, and 7 is 7430. To arrive at this number, we rearrange the digits in descending order, placing the highest digits at the more significant places. Since we cannot start with 0 in a 4-digit number, we position 3 and 0 towards the end.
On the other hand, the smallest 4-digit number formed using these digits is 3047. Here, we must ensure that the first digit is not 0, so we start with the next highest digit, which is 3, followed by the remaining digits arranged in ascending order.