To find all of the possible group sizes for the 32 students, we need to find the factors of 32. A factor of a number is a number that divides evenly into that number.

Let's find the factors of 32:

The prime factorization of 32 is $2^5$. The factors are the numbers that divide 32 without leaving a remainder. These are:

1, 2, 4, 8, 16, and 32.

Thus, the possible group sizes for the 32 students are 1, 2, 4, 8, 16, and 32.

Since the condition is that no student can be in a group alone, the group size of 1 isn't allowed.

So, the valid group sizes are: 2, 4, 8, 16, and 32.

Would you like to know more details or have any questions? Here are some related questions:

1. How do you find the factors of any number?
2. What is the significance of prime factorization when determining factors?
3. Can a number have more than one set of factors?
4. How do divisors relate to multiplication?
5. What is the greatest common divisor (GCD) of two numbers?

Tip: If you ever need to find the factors of a number quickly, you can list the divisors starting from 1 and test up to the square root of the number.