This task is from Tools for NC Teachers. Students consider all of the possible ways to arrange chairs into equal groups.  This is remixable.

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Part 1:

There are 24 chairs in the art room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group?  How do you know that you have found every arrangement?  Write equations to show your answers.

 Part 2:

There are 48 chairs in the multi-purpose room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group?  How do you know that you have found every arrangement?  Write equations to show your answers.

 Part 3:

What relationship do you notice about the size of the groups if the chairs were arranged in 4 groups in both Part 1 and Part 2?  What about if the chairs were arranged in 8 groups?  Explain why you think this relationship exists.