I was wondering if there was a way to logically/mathematically derive what the smallest possible largest prime factor to a number was, using each of the digits 1-9 only once.
An example could be 123456789, which has a largest prime factor of 3803.
I tried 164385792 by experimenting with the exponent of 2, but that came out with 17837.
Is there a way to find the minimum largest prime factor without using brute force?