1. **State the problem:** We have 12 oranges that need to be divided into bags. Each bag must have the same number of oranges. Each bag must contain more than one orange. There must be more than one bag. 2. **Identify conditions:** Let the number of oranges per bag be $x$. Let the number of bags be $y$. Since all oranges must be used, we have the equation: $$ x \times y = 12 $$ With constraints: $$ x > 1 $$ $$ y > 1 $$ 3. **Find all factor pairs of 12:** The positive factor pairs are: $$ (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), (12, 1) $$ 4. **Apply constraints to factor pairs:** Both $x$ and $y$ must be greater than 1, so remove pairs with 1. Remaining pairs are: $$ (2, 6), (3, 4), (4, 3), (6, 2) $$ Since the problem states each bag has the same number ($x$), possibilities for $x$ are the first elements in these pairs: $$ x = 2, 3, 4, 6 $$ 5. **Conclusion:** The number of oranges per bag could be 2, 3, 4, or 6. **Final answer:** $$ \boxed{2, 3, 4, 6} $$