Do I have any hope of getting a home loan?

I have a credit score of about 620...it is this low because my ex and i had a car loan together. After separating he kept the car and had it repossessed several times. I paid off the car to get it off my name and the divorce decree says he is responsible. Otherwise everything is paid off every month and income to debt ratio is excellent. Is it possible to get a home loan? What is the minimum score? with companies look past this one fault if i provide documentation?