How would one go about finding all 3-digit positive integers $ \overline{abc}$ with the property $\overline{abc}=abc(a+b+c)$, where $ \overline{abc}$ would be the decimal representation of a number.
I have tried reducing to algebra, where one gets $100a+10b+c=abc(a+b+c)$, but i am at a complete loss as to what to do next!