A teacher has a class with $24$ students in it. If she wants to split the students into equal groups of at most $10$ students each, what is the least number of groups that she needs?
To split the students into equal groups, the number of students in each group must be a factor of $24$. The factors of $24$ are $1, 2, 3, 4, 6, 8, 12, 24$. However, the teacher wants the groups to have at most $10$ students each, so we can eliminate $12$ and $24$ as possible group sizes. The largest remaining factor is $8$, so if she splits the class into groups of $8$ students each, she will use the least number of groups. To find the number of groups, we divide the total number of students by the group size: $24 \div 8 = 3$. Therefore, the least number of groups that she needs is $3$. 