The exact number of national championships won by the University of Kansas across all sports is difficult to definitively state due to variations in how different organizations track and recognize championships (e.g., different governing bodies, different eras, etc.). There's no single, universally agreed-upon official count.
However, the University of Kansas itself often cites a number in the high 30s or low 40s. This figure includes championships across all men's and women's sports and accounts for different levels of competition. You'll find slightly different numbers depending on the source and the criteria used.