Arjun uses all 12 counters to make rectangles (3 rows of 4 and 4 rows of 3 count as the same). Two are shown. How many different rectangles can he make in all, and is 12 prime or composite?

Question

Accepted Answer

3; composite. 12 = 1 × 12 = 2 × 6 = 3 × 4 , so 3 rectangles; the missing one is 3 rows of 4. A number that makes more than one rectangle has factors other than 1 and itself, so 12 is composite.

Arjun uses all 12 counters to make rectangles (3 rows of 4 and 4 rows of 3 count as the same). Two are shown. How many different rectangles can he make in all, and is 12 prime or composite?

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