Question: 28 students are on a school trip.
They need to split into smaller groups of equal size.
No student can be in a group alone.
Find all of the possible group sizes.
1. **State the problem:** We have $28$ students who need to be divided into groups of equal size.
2. **Important rule:** Each group must have more than one student (no group of size $1$).
3. **Mathematical approach:** We need to find all divisors of $28$ greater than $1$ because the group size must divide $28$ exactly.
4. **Find divisors of $28$:**
$$28 = 1 \times 28 = 2 \times 14 = 4 \times 7$$
5. **List all divisors:** $1, 2, 4, 7, 14, 28$
6. **Exclude group size $1$:** Because no student can be alone.
7. **Possible group sizes:** $2, 4, 7, 14, 28$
8. **Interpretation:** The students can be split into groups of size $2$, $4$, $7$, $14$, or all $28$ in one group.
**Final answer:** The possible group sizes are $2$, $4$, $7$, $14$, and $28$.