There are 435 seniors at a high school and they are all placed in groups consisting of more than 2 students but fewer than 30 students.

Question

There are 435 seniors at a high school and they are all placed in groups consisting of more than 2 students but fewer than 30 students. Each group is to have an equal number of students and each student is to be in only one group. List all of the group sizes that are possible. How many groups are there of each size?

Answer 1

The question can be rephrased in this way: which integers strictly between 2 and 30 (in other words, not = 2 and not = 30) are factors of 435?

435 = 3·5·29 , which is its prime factorization.

Thus, we could have 3 groups of 145 students, or 145 groups of 3. We could have 5 groups of 87, or 87 groups of 5. 29 groups of 15, or 15 groups of 29.