How much time it takes to heal broken bone with out any treatment?

Depends on the: Nature of the break. Some bones may be comminuted and in multiple pieces, location is important as well, some anatomical locations will take longer to heal I.e jones fracture of fifth metatarsal with no treatment likely will take longer......I would advise proper treatment.

On average 6-8 weeks: There are several factors that can affect healing a broken bone...severity of the break, bone that is broken, existing medical problems and how controlled they are (ie diabetes, thyroid disease, osteopenia, osteoporosis, low vitamin D, etc.), as well as smoking history. On average, it takes a simple fracture 6-8 weeks to heal. Sometimes longer if any of the above listed conditions exist.