Follow the instructions to find factorizations for several numbers. As you work, see if you can answer these questions:
- Why do you think the length and width of the rectangles represent the factors of your numbers?
- Which number has the most factorizations? Which has the fewest? Why do you think this is?
- What kinds of numbers have only one factorization? What do the rectangles for these factorizations have in common?
- If you double a number, what happens to the number of
factorizations? Do you notice a pattern in the factorizations of your
original number and the doubled number?