Find a six digit integer Find an integer with six different digits such that the six digit integer is divisible by each of its digits.
For example, find ABCDEF such that A, B, C, D, E and F all can divide the number ABCDEF.
Show your answer along with mathematical reasoning.

The highest match is 984312
I wrote a quick Python3 script to find all the matches:
for number in range(100000, 1000000):
    string = str(number)
    digits = []
    unique = True

    for ch in string:
        if ch in digits:
            unique = False
            break
        else:
            digits.append(ch)

    if not unique: # If the digits are not unique, move to the next iteration
        continue

    if all([False if digit == '0' else number % int(digit) == 0 for digit in str(number)]):
        # Number divides perfectly with every digit
        print(number)

This code will print every working number, each to a new line.
